Question
Asked Oct 15, 2019

A motorboat traveling with the current went 105 mi in 5 h. Traveling against the current, it took 7 h to travel the same distance. Find the rate of the boat in calm water and the rate of the current.

rate of boat     mph
rate of current     mph
check_circleExpert Solution
Step 1

Let x be the speed of the motorboat in still water and y be the speed of the current.

The rate of motorboat traveling with current is, x + y.

Given that the boat travelling with the current went 105 mi in 5 h.

It is known that, speed is equal to quotient of distance and time.

Use the speed formula to find the unknowns as follows.

Distance speedx time
105= 5x (xy)
-(1)
x+y 2
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Distance speedx time 105= 5x (xy) -(1) x+y 2

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Step 2

The rate of motorboat traveling against the current is, x y.

Given that the boat travelling against the current took 105 mi in 7 h.

Use the speed formula to find the unknowns as follows.

Distance speed x time
105 7x(x-y
(2)
x-y15
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Distance speed x time 105 7x(x-y (2) x-y15

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Step 3

Add equation (1) and (2) results, 2x = 36.

Therefore, x = 18.

Sub...

18+y 21
y =21-18
= 3
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18+y 21 y =21-18 = 3

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