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

Answer:

5 miles per hour and 15 miles per hour.

Step-by-step 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, $Distance = speed\times time$

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

$x\times2 + (4x-5)\times6 = 100\\2x +24x-30=100\\26x-30 =100$

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 = $4x-5$ =$4\times5-5 =20 -5 = 15 \ miles\ per \ hour$

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