Problema Solution
At 5 AM, a boy rides his bike due north from campus at 14 mph. Two hours later, another boy rides his bike due east from the same point, also at 14 mph. When will they be 140 miles apart?
Answer provided by our tutors
Let
x = the time that the first boy travels at 14 mph
x - 2 = the time the second boy travels at 14 mph
140 the distance between them
Since one travels north and the other east (their roads are perpendicular) the distance between them can be calculated using Pythagorean Theorem
(14*x)^2 + ((x-2)*14)^2 = 140^2
the solutions of the quadratic equation are
x1 = - 6 is not the solution since x > 0
x2 = 8 h is the solution
They will be 140 miles apart 8 hours after the first boy started the trip or 6 hours after the second boy started the trip.