Refer a friend and earn $50 when they subscribe to an annual planRefer Now
Get the answer to your homework problem.
Try Numerade Free for 30 Days
Like
Report
Megan traveled 165 miles to visit friends. On the return trip she was delayed by construction and had to reduce her average speed by 22 miles per hour. The return trip took 2 hours longer. What was the time and average speed for each part of the trip?
Initial trip: 55 $\mathrm{mph}$ and 3 hoursReturn trip: 33 $\mathrm{mph}$ and 5 hours
Algebra
Chapter 4
RELATIONS AND FUNCTIONS
Section 10
Inverse Variation
An Introduction to Geometry
Functions
Linear Functions
Polynomials
Oregon State University
Harvey Mudd College
Lectures
01:32
In mathematics, the absolu…
01:11
A couple traveled at an av…
02:42
Distance, Speed, and Time …
03:02
In Exercises 21–36, write …
01:37
Paul drove from his house …
03:24
Jim drove 306 miles. Jim&#…
01:28
On a trip, Corrine left at…
01:49
Solve each problem. Margar…
02:48
A plane left Kennedy Airpo…
02:46
A cyclist rides at an aver…
03:04
Julie drives 100 mi to Gra…
for this problem. There's a pursued use traveling 165 miles total and were given that on the way back there speed decreases by 22 their time increases by two hours. So we can set up a equation to equations actually, better going to be ours equal to ours. And we'll get that by multiplying miles per hour, times, hours, and then just setting. Um then oh, we're setting actually miles, two miles. So it would just be like distance is equal to distance. So we multiply in miles per hour by ours, we get miles, and then we're giving a miles. So let me start with 1 65 which is are known, and we know that that's just equal to the initial speed. I'll call initial Speed s Times the initial time that it took. So that's t. And on the other equation that we use is 1 65 is equal to like the way back. So this is the way back equation. So we do s minus 22 times T plus two. So if we were to substitute the first equation into the second equation, we that probably the best way to do is with us. So those two s is equal to 1 65 over T. And so if I was to put that in, I get 1 65 is equal to 1 65 T minus 22 times T plus two. It's probably easiest to multiply both sides, but a t So if I multiply them by T, I'll get 1 65 t is equal to I'll put the tea into this first term here, so I'll get 1 65 Why is 22 t And since I distributed the tea in the first term, I don't have to distribute it in the second term cause of on the community property, so it just stays the same. So if I was to distribute this hour, I get 1 65 t sequel to 1 65 T minus 22 t squared. Um, plus, I'm actually minus 20 Li aa plus. So I did first Terrorism, tens. First term. I did second term trans first term. I mean, he first turned time second terms. That's two times 1 65 and then second term physic in term is minus 40 40. So these two terms. Cancel out. And if I'm a bit to the right side, I get 22 t squared plus 44 t minus, um, 3 30 which is two times 1 65 is equal to zero. And so there's a common devices here that is 22. So if I pull that, I get t squared plus to t minus 15 this equal to zero. And so if I use, um, factoring, I'll get three and five as the numbers of monies. And in order to fix the signs, I'll use this one and this one it is equal to zero. So you get that The initial time taking was three hours. We can't use the other one because it will be negative. So this is tthe e real answer for initial time. So it's a t T. Initial three hours s initial is 1 65 divided by three, which comes out to 55 uh, Mph. And then for a T final, it's ah, two more. So be five hours and because it's in the same proportion s as final will be 33 and ph
View More Answers From This Book
Find Another Textbook
Numerade Educator
In mathematics, the absolute value or modulus |x| of a real number x is its …
A couple traveled at an average speed of $52 \mathrm{mph}$ for a cross-count…
Distance, Speed, and Time Wendy took a trip from Davenport to Omaha, a dista…
In Exercises 21–36, write an equation for the problem and solve the problem.…
Paul drove from his house to work at an average speed of 40 miles per hour. …
Jim drove 306 miles. Jim's brother made the same trip at a speed 17 mil…
On a trip, Corrine left at 7 A.M. and traveled 152 miles, then took a 15 -mi…
Solve each problem. Margaret drove to a business appointment at 50 mph. Her …
A plane left Kennedy Airport on Tuesday morning for a 605 mile, 5 -hour trip…
A cyclist rides at an average speed of 18 mi per hour. If she wants to bike …
Julie drives 100 mi to Grandmother's house. On the way to Grandmother&#…
00:42
Explain the difference between fg $(x)$ and $f(g(x))$
00:53
In $35-43,$ write each number in simplest form.$$i+i^{2}+i^{3}+i^{4}…
00:44
In $23-28,$ write an equation of the direct variation described. Water i…
01:26
Does $y=x^{2}$ have an inverse function if the domain is the set of real num…
01:03
In $3-14$ , use the quadratic formula to find the roots of each equation. Ir…
02:41
In $3-38,$ solve each equation for the variable, check, and write the soluti…
02:09
The roots of a quadratic equation with rational coefficients are $p \pm \sqr…
03:23
Ian often buys in large quantities. A few months ago he bought several cans …
00:37
In $3-41$ , express each product in simplest form. Variables in the radicand…
01:55
In $38-45,$ find the multiplicative inverse of each of the following in $a+b…
92% of Numerade students report better grades.
Try Numerade Free for 30 Days. You can cancel at any time.
Annual
0.00/mo 0.00/mo
Billed annually at 0.00/yr after free trial
Monthly
0.00/mo
Billed monthly at 0.00/mo after free trial
Earn better grades with our study tools:
Textbooks
Video lessons matched directly to the problems in your textbooks.
Ask a Question
Can't find a question? Ask our 30,000+ educators for help.
Courses
Watch full-length courses, covering key principles and concepts.
AI Tutor
Receive weekly guidance from the world’s first A.I. Tutor, Ace.
30 day free trial, then pay 0.00/month
30 day free trial, then pay 0.00/year
You can cancel anytime
OR PAY WITH
Your subscription has started!
The number 2 is also the smallest & first prime number (since every other even number is divisible by two).
If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".
Receive weekly guidance from the world's first A.I. Tutor, Ace.
Mount Everest weighs an estimated 357 trillion pounds
Snapshot a problem with the Numerade app, and we'll give you the video solution.
A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.
Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.