gmatt14 wrote:

Hi everybody.

A boat travels up the river and down the river the same distance. If the average relative speed of the boat 48 mph and the speed of the river is 10 mph, what is the upriver speed of the boat?

My solution:

Up stream the boat must be 10 mph slower than average. So I came up with 38 mph.

However, the correct answer is: 40 mph.

Can anybody explain?

40 is correct, average speed = total Distance/total Time

Let speed of boat = \(x\)

upstream speed = \(x-10\)

downstream speed = \(x+10\)

total distance covered = \(2y\)

time taken upwards = \(\frac{y}{{x-10}}\)

time taken downwards =\(\frac{y}{{x+10}}\)

total time = \(\frac{y}{{x-10}} + \frac{y}{{x+10}}\)

average speed = \(\frac{2y}{{{y/(x-10)}+ y/(x+10)}} = \frac{{x^2-100}}{x}= 48\)

=> \(x^2 - 48x - 100 = 0\)

= \((x-50)(x+2) = 0\), x cannot be -ve thus\(x=50\)

upstream speed =\(x-10 = 50-10 = 40\)

PS: 48 is the average relative speed.

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