Question

A motorboat maintained a constant speed of 1010 miles per hour relative to the water in going 1212 miles upstream and then returning. The total time for the trip was 2.52.5 hours. Use this information to find the speed of the current.

Answer 1

Answer: the speed of the current is 202 mph

Explanation:

Let x represent the speed of the current.

Miles travelled while going upstream is 1212

Miles travelled while going downstream is 1212

Assuming the motor boat travelled against the wind while going upstream, the speed would be

(1010 - x) mph

Assuming the motor boat travelled with the wind while going downstream, the speed would be

(1010 + x) mph

Distance = speed × time

Time = distance/speed

Time it took upstream is

1212/(1010 - x)

Time it took downstream is

1212/(1010 + x)

Total time for the trip is 1.5 hours. It means that

1212/(1010 - x) + 1212/(1010 + x) = 2.5

Cross multiplying by (1010 -x)(1010 + x), it becomes

1212(1010 + x) + 1212(1010 - x) =

2.5(1010 - x)(1010 + x)

1224120 + 1212x + 1224120 - 1212x = 2.5(1020100 + 1010x - 1010x - x²)

2448240 = 2550250 - 2.5x²

2.5x² = 102010

x² = 102010/2.5

x² = 40804

x = √40804

x = 202 mph

Answer 2

2.0 mph

Explanation:

Considering a straight-line displacement, the current has a velocity acting on the same axis at which the motorboat is traveling. Assume that the current's velocity is positive in the downstream leg of the trip, the velocity of the current can be determined by:

`U: (V_(boat) - V_(current))*t_U=12\\D: (V_(boat) + V_(current))*t_D=12\\t_U +t_D = 2.5 = (12)/(10 - V_(current))+(12)/(10 + V_(current))\\2.5*(10^2-V_(current)^2)=120 -12V_(current)+120+12V_(current)\\-2.5V_(current)^2 +250 = 240\\V_(current)=\sqrt{(10)/(2.5)}\\V_(current) = 2\ mph`

The speed of the current is 2 miles per hour.