Alan works 6miles away from the apartment and rollerblades from his work place to the apartment at a constant rate of 7miles per hour. Soren works 8 miles away from the apartment and bikes from his work place at a constant rate of 12miles per hour. How much time in hours do Alan and Soren have to travel to be the same distance from their apartment?

Question

Huerta

Mathematics

15 July, 08:03

Alan works 6miles away from the apartment and rollerblades from his work place to the apartment at a constant rate of 7miles per hour. Soren works 8 miles away from the apartment and bikes from his work place at a constant rate of 12miles per hour. How much time in hours do Alan and Soren have to travel to be the same distance from their apartment?

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Grace Robinson · Answer 1

Let the distance remaining after time t be x miles.

Distance traveled by Alan = (6-x) miles

Distance traveled by Soren = (8-x) miles

Time takes by the two is the same. Therefore,

(8-x) / 12 = (6-x) / 7 = > 7 (8-x) = 12 (6-x) = > 56-7x = 72-12x = > 12x-7x = 72 - 56 = > 5x = 16 = > x = 16/5 = 3.2 miles.

And then, time taken (t) = (8-3.2) / 12 = (6-3.2) / 7 = 0.4 hours