A boat takes 7.5 hours to make a 60-mile trip upstream and 6 hours on the 60-mile return trip. Let v be the speed of the boat in still water and c be the speed

Question

A boat takes 7.5 hours to make a 60-mile trip upstream and 6 hours on the 60-mile return trip. Let v be the speed of the boat in still water and c be the speed of the current.

Answer 1

Hey Carson. I'm going to guide you along the steps but I'm going to leave the calculations.

 

So, this is a rate problem where the rate is expressed by two variables: v and c. v is the boat speed, c is the speed of the current.

You have two distance equations which both describe the upstream journey and the downstream journey. So instead of: Distance = speed * time

 

You have for the upstream journey:
60 miles = (v - c) * 7.5 hours since the current and the boat are going in opposite directions.

For the downstream journey:
60 miles = (v + c) * 6 hours since the current and the boat are going in the same direction.

You can divide the 60 miles by the 7.5 hours and the 6 hours in both equations to get to two simplified equations:

7.5 miles/hour = v - c
and:
10 miles/hour = v + c

So now you have 2 equations with 2 unknowns.

I believe you can figure it out from here :)