It took Ellen 6 hours to ride her bike a total distance of 120 miles. For the first part of the trip, her speed was constantly 25 miles per hour. For the second part of her trip, her speed was constantly 15 miles per hour. For how many miles did Ellen travel at 25 miles per hour?a. 60
b. 62.5
c. 66 2/3
d. 75
e. 90

Ellen traveled 75 miles at 25 miles per hour.

Step-by-step explanation:

Let x represent the number of miles that she travelled at 25 miles per hour.

If the total distance that she covered is 120 miles, then the distance that she covered at 15 miles per hour is (120 - x) miles

Time = distance/speed

Time taken to travel at 25 miles per hour is expressed as

x/25

Time taken to travel at 15 miles per hour is expressed as

(120 - x)/15

Since the total time for the trip is 6 hours, it means that

x/25 + (120 - x)/15 = 6

Multiplying both sides of the equation by 75, it becomes

3x + 5(120 - x) = 450

3x + 600 - 5x = 450

3x - 5x = 450 - 600

- 2x = - 150

x = - 150 / - 2

x = 75