Question

Isabella and Tanner are running in a 100-mile relay race. First, Isabella runs for 2 hours and hands off to Tanner, who bicycles for 6 hours to the finish line. If Tanner's average cycling speed is 5 miles an hour less than 4 times Isabella's average running speed, what are their 2 speeds?

Answer 1

5 miles per hour and 15 miles per hour.

Explanation:

Given:

Isabella and Tanner are running in a 100-mile relay race.

First, Isabella runs for 2 hours and hands off to Tanner, who bicycles for 6 hours to the finish line.

Tanner's average cycling speed is 5 miles an hour less than 4 times Isabella's average running speed.

Question asked:

what are their speed ?

Solution:

Let average running speed of Isabella =
`x`

Tanner's average cycling speed is 5 miles an hour less than 4 times Isabella's average running speed means,

Tanner's average cycling speed =
`4x-5`

Now,
`Distance = speed* time`

As we know that the total distance is 100 mile which is covered by both together,

Distance traveled by Isabella + Distance traveled by Tanner = 100

`x*2 + (4x-5)*6 = 100\\2x +24x-30=100\\26x-30 =100`

Adding both sides by 30

`26x =1 30\\`

Dividing both sides by 26

`x=5`

Isabella's average running speed
`x=5 \ miles \ per \ hour`

Tanner's average cycling speed =
`4x-5` =
`4*5-5 =20 -5 = 15 \ miles\ per \ hour`

Therefore, Isabella's average running speed is 5 miles/hour and Tanner's average cycling speed is 15 miles/hour.