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In his​ motorboat, Tran travels upstream at top speed to his favorite fishing​ spot, a distance of 54 ​miles, in 6 hours.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 4.5 hours. Find the speed of​ Tran's boat and the speed of the current.

Sagot :

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Step-by-step explanation:

D = rate x time

D = (rate of current + rate of boat) x time

168 = (y - x) t against the current trip upstreams

168 = (y + x) t with the current trip downstream

168 = (y - x) 4

168 = (y + x) 3.5

since 168 = 168, we can set the equations equal to each other:

(y - x)4 = (y+x)3.5

4y - 4x = 3.5y +3.5x

4y - 3.5y = 3.5x + 4x

0.5y = 7.5x

y =15x

the rate of the current is 15 times the rate of the boat.

168 =4(15x) - 4x

168 = 60x - 4x

168 = 56x

x = 3

y = 15x

y = 15(3)

y = 45

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