Question

Clem Shirestock is at a dock on a bank of a straight river that is 1 mile wide and wants toreach the barge toll gate on the other side, so he can warn the guards about the stolengoods on an approaching barge. The toll gate is 4 miles downstream on the opposite bank,and Clem want to get there by first rowing his boat to somewhere (call it point P) on theopposite bank and then walking the remaining distance * to the toll gate. He can row at 4mph and walk at 2 mph. Express the total time 7, in terms of x, that he takes to go from thedock to the toll gate.

Answer 1

The total time taken by Clem Shirestock to reach the gate is given by the  equation 7 = 4√(x²+1)+ 8 - 2 x

Let the point P is at a distance of x miles from the toll gate.

Hence when Clem reaches the point P he rows in the form of right angled triangle. and we know that the width of the river is 1 mile.

So by using Pythagoras Theorem we can infer that the distance covered by Clem is the hypotenuse which is equal to √(x²+1).

Time taken to complete this route is  4√(x²+1) .

Now  he has only to walk 4-x distance along the river.

His speed is 2 mph

Time taken = 2(4-x) = 8-2x

Hence we can conclude that the total time is 7 hours. so the equation to represent this is 7 = 4√(x²+1)+ 8 - 2 x .

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