Question

Two friends collectively travel 1,700 miles to see each other. They fly toward each other to meet for a weekend. The first friend flew on an airplane and it took her 2 hours to meet her friend. The second friend leaves 15 minutes later, but her plane flew 25 miles per hour faster than her friend's plane. The planes arrive at the airport at the same time. What was the second friend's speed, to the nearest whole number? ​

Answer 1

The second friend's airplane speed was 467 miles/hr.

Explanation:

The total distance travelled, 1700 miles, is comprised of the distance each friend flies. The distance is the product of the time flying times the speed of the aircraft. The distance for each friend is:

Friend Time(h) Speed(m/h) Distance(m)

1 2 x 2x

2 1.75 x + 25 1.75*(x + 25) or

1.75x + 43.75

Note that the time Friend 2 spends flying is 15 minutes less than Friend 1 since the planes arrive at the same time, but Friend 2 left 15 minutes, or 0.25 hours, after Friend 1 left.

The total distance travelled by the friends is 1,700 miles, since they meet at some point between the two starting points. We can then write:

(2h)x + (1.75h)x + 43.75) = 1,700 miles

(3.75h)x + 43.75 miles = 1,700 miles

x = (1656.25 miles)/(3.75 h)

x = 441.67 m/h

Friend 1 flew at a speed of 441.57 m/h

Friend 2 flew at a speed of x + 25 or 466.6667 or 467 m/h

CHECK:

Do the two airplane speeds and times amount to a total distance of 1,700 miles?

Friend 1: (441.67 m/h)(2 h) = 883.3 miles

Friend 2: (467 m/h)*(1.75 h) = 816.7 miles

Total = 1,700 miles YES