A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of 60mph. Two hours later, a special agent in a helicopter starts chasing the spy. The special agent travels the same route at a speed of 90mph. *At what speed Chapter Reference should the special agent chase the spy if the evacuation spot is 240 miles from the starting point?

Question

A spy realizes his cover is blown and flees toward his secret evacuation spot at a speed of  60mph. Two hours later, a special agent in a helicopter starts chasing the spy. The special agent travels the same route at a speed of  90mph. *At what speed Chapter Reference should the special agent chase the spy if the evacuation spot is 240 miles from the starting point?

Bytelearn · Accepted Answer

Calculate Distance Traveled: Determine the distance the spy has traveled before the special agent starts chasing. The spy starts 2 hours earlier at a speed of 60 mph. Distance = Speed × Time Distance = 60 mph × 2 hours Distance = 120 milesCalculate Remaining Distance: Calculate the remaining distance to the evacuation spot after the spy has traveled for 2 hours. Total distance to evacuation spot = 240 miles Distance traveled by spy = 120 miles Remaining distance = Total distance - Distance traveled by spy Remaining distance = 240 miles - 120 miles Remaining distance = 120 milesDetermine Time to Catch: Determine the time it would take for the special agent to catch up to the spy. Since the spy is already on the move, the special agent needs to cover the remaining distance plus the distance the spy continues to travel. Let t be the time in hours it takes for the special agent to catch the spy. In that time, the spy travels an additional 60 mph × t miles. The special agent travels 90 mph × t miles. Since the special agent catches up to the spy, their distances traveled will be equal. 60 mph × t + 120 miles = 90 mph × tSolve Equation for t: Solve the equation for t. 60t + 120 = 90t 120 = 90t - 60t 120 = 30t t = 120 / 30 t = 4 hoursCalculate Total Distance: Calculate the total distance the special agent must travel to catch the spy. The special agent travels at 90 mph for t hours. Distance = Speed × Time Distance = 90 mph × 4 hours Distance = 360 milesDetermine Required Speed: Determine the speed the special agent must maintain to reach the evacuation spot in time. The special agent must travel 360 miles to catch the spy, and the evacuation spot is 240 miles from the starting point. Since the special agent catches the spy before reaching the evacuation spot, the speed to reach the evacuation spot is not relevant to catching the spy. The special agent must maintain the speed of 90 mph to catch the spy before the spy reaches the evacuation spot.

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