7) The senior classes at High School A and High School B...

7) The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled 4 vans and 14 buses with 594 students. High School B rented and filled 6 vans and 7 buses with 345 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? 8) A boat traveled 336 miles each way downstream and back. The trip downstream took 12 hours. The trip back took 24 hours. What is the speed of the boat in still water? What is the speed of the current?

Transcript

00:01 So in this problem, we're told that a boat traveled a total of 336 miles downward and back, meaning 336 miles down as well as 336 miles back.

00:10 Now, we're told that the time downstream took 12 hours, and the time upstream took 4 hours, 14 hours.

00:16 So what we're being asked to do is find the speed of the boat in still water as well as the speed of the current.

00:21 So we're looking for two things.

00:23 So we're going to need two different variables.

00:24 So i'm going to let s represent the speed in still water.

00:32 And then we're going to let c represent the speed of the current.

00:37 And they even gave you a hint here to set up a table.

00:40 Now keep in mind that distance is equal to rate times time.

00:44 So that's exactly what we're going to do.

00:46 So we're going to have rate times to time, and that will equal the distance.

00:49 So we have these two different options.

00:51 So one of our trips, we're going downstream.

00:54 And the other one, we're going upstream.

00:56 Now, let's first talk about our rate going down.

00:59 Well, think about it.

01:00 If we're going downstream, the current is going to push us, which is going to make us faster, meaning we would be the speed and still water, which is s, plus we would add on the current.

01:11 Now, the time going downstream.

01:13 Well, we were told that it takes 12 hours to go downstream.

01:16 So our second column would have 12.

01:18 And it equals, well, we know the total distance was 336.

01:22 Okay, well, now let's talk about the trip upstream.

01:25 Well, if you're going upstream, the current is going to slow you down, meaning you would take your speed in still water and subtracted by the current speed, which is c.

01:33 Then we have the time that it takes to go upstream, which is 14 hours.

01:37 And again, we knew our total distance was equal to 336...

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