Question

A boat's crew rowed 10.5 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covering the same distance, but took 3.5 hours. Find the crews rowing rate in still water and the rate of the current

Answer 1

let the crew's rowing rate be r and let the rate of the current be c.
Distance = speed * time.
Considering the downstream journey we can write:
10.5 = (r + c) * 1.5 ..........(1)
Removing the brackets in (1) gives:
10.5 = 1.5r + 1.5c ..........(2)

Considering the upstream journey we can write:
10.5 = (r - c) * 3.5 .........(3)
Removing the brackets in (3) gives:
10.5 = 3.5r - 3.5c ..........(4)

Equations (2) and (4) are a simultaneous pair that can be solved to find the values of r and c.
Do you follow so far?

Answer 2

yes

Answer 3

Good! Equation (2) can be arranged to give r in terms of c as follows:
10.5 = 1.5r + 1.5c ..........(2)
Rearranging (2) we get
1.5r = 10.5 - 1.5c .........(5)
And dividing both sides of (5) by 1.5 gives:
r = 7 - c .............(6)
Now we can plug the expression for r in equation (6) into equation (4) giving:
10.5 = 3.5(7 - c) - 3.5c ..............(7)
This means you can solve equation (7) to find the value of c. When you have the value of c, just plug it into (2) and solve for the value of r.

Answer 4

thanks

Answer 5

You're welcome :)