Question

A rowing team rowed 60 miles while going with the current in the same amount of time as it took to row 10 miles going against the current. The rate of the current was 5 miles per hour. Find the rate of the rowing team in still water.

Answer 1

Answer:

7 miles per hour

Step-by-step explanation:

Data:

Rate of current = 5 miles / hr

The solution to this problem is in two parts:

1) Rowing team going with the current covering 60 miles

2) Rowing team going against the current covering 10 miles

The formula used to calculate rate will be :

Velocity = $\frac{Distance}{time}$ = v =$\frac{S}{t}$

1) Rowing team going with the current covering 60 miles

Distance = S = 60 miles

Rate = velocity = Rate of Current + Rate of rowing team = $v_{1} + v_{2}$ = 5 + $v_{2}$  

using the velocity formula:

5 + $v_{2}$  = $\frac{60}{t}$ --------------------- Equation. 1

2) Rowing team going against the current covering 10 miles

Distance = S = 10 miles

As the current is against the direction of rowing team so the rate of current will be subtracted from the rate of rowing team.

Rate = velocity = Rate of rowing team - Rate of Current  = $v_{2} - v_{1}$ =  $v_{2}$  - 5

Using velocity formula:

$v_{2}$  - 5 = $\frac{10}{t}$

                                                                                                   

Cross multiplying

t = (10) ÷ ($v_{2}$  - 5)

put this in equation 1.

we get :

5 + $v_{2}$  = ($\frac{60}{10}$) $v_{2}$  - 5

5 + $v_{2}$ = (6)  $v_{2}$  - 5

5 + $v_{2}$ =  $6v_{2}$  - 30

5 + 30 =   $6v_{2}$ -  $v_{2}$

35 = $5v_{2}$

$v_{2}$ = $\frac{35}{5}$

$v_{2}$ = 7 miles/hr

rate of the rowing team boat in still water=7 miles/hr