Question

A plane Airport on Tuesday morning for a 755-mile,6- hour trip. For the first part of the tripthe average speed was 105 mphFor the remainder of the trip the average speed was 130 mph . How long did the plane fly at each speed ?

Answer 1

105 miles / hour for 1 hour

130 miles / hour for 5 hours

Explanation:

Part A

• speed = 105 mph
• distance = x
• time = y

Part B

• speed = 130 mph
• distance = 755 miles - x
• time = 6 hr - y

plane Part A: x = 105 *y

Plane Part B: 755 - x = 130*(6 - y)

Put 105*y into the equation for plane B

755 - 105*y = 130*(6- y) Remove brackets on the the right.

755 - 105y = 780 - 130y Add 130y to both sides

755 - 105y + 130y = 780 Combine left

755 + 25y = 780 Subtract 755 from both sides

25y = 780 - 755

25y = 25 Divide by 25

y = 25/25

y = 1

The plane travelled 1 hour at 105 mile / hour

The plane travelled 5 hour at 130 mile / hour

Check

1 hour for a distance of 1 hr * 105 mph = 105 mile

5 hour for a distance of 5 hr*130 mph = 650 miles

Total distance = 755 miles

Remark

This is a very neat problem. I don't think I've ever seen this variation. It is a little long, but it is well worth your time.