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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
Two vehicles start simultaneously from city A towards city B. The distance between the cities is 278.4 miles. The first vehicle travels at a speed that is 5 miles per hour greater than the speed of the second one and, for this reason, it arrives 2 hours earlier in city B. What is the speed of the second vehicle?
If the motion is uniform rectilinear, the distance is equal to the product between time and speed. We apply this law of motion for each of the two vehicles:
We apply the supplementary information given by the problem, to find:
Subtract the two last equations:
Substituting back in one of the equations for the distance:
Solving this quadratic equation, we retain only the positive solution:
We can now find the required velocity by back-substitution: