Question

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?

Answer 1

Define x:

Let x be the number of hours taken for the first part of the race

The second part of the race = (1.125 - x ) h

First part of the race:

Speed = 8 miles/hour

Time = x

Distance = Speed x Time

Distance = 8x miles

Second Part of the journey:

Speed = 20 miles/hour

Time = 1.125 - x

Distance = Speed x Time

Distance = 20 ( 1.125 - x) miles

Solve x:

Total distance = 15 miles

8x + 20 (1.125 - x) = 15

8x + 22.5 - 20x = 15

12x = 7.5

x = 0.625 hour

Find the time:

First Part of the journey = x = 0.625 hour

Second Part of the journey = 1.125 - x = 1.125 0 0.625 = 0.5 hour

Find the distance:

First Part of the race = 8x =  8(0.625) = 5 miles

Second Part of the race = 20(1.125 - x) =  20( 1.125 - 0.625) = 10 miles

Answer:

First Part of the Journey (Run):

Rate = 8 miles per hour

Time = 0.6 hour

Distance = 5 miles

Second Part of the journey:

Rate = 20 miles per hour

Time =  0.5 hour

Distance = 10 miles

Answer 2

Let the distance be of the first part = x, the second part be = 15-x, then x/8 + 15 – x /20 = 1.225 x + 2 (15x) = 1.225x x 40 +30-2x= 453x, 45-30=15x, 15/3=.

Therefore the distance of the first race is 5 miles.

Time is 5/8=0.625 hours. The distance of the second part race is 15-5= 10 miles.

The time is 1.125-0.625= 0.5 hours or 30 minutes.