In a 10 mile race, Janet covered the first 2 miles at a constant rate. She then sped up and rode her bike the last 8 miles at a rate that was 0.5 miles per minute faster. Janet's overall time would have been 2 minutes faster had she ridden her bike the whole race at the faster pace. What was Janet's average speed (in miles per minute) for the whole race?

Step-by-step explanation:

GIVEN: In a mile race, Janet covered the first miles at a constant rate. She then speed up and rode her bike the last miles at a rate that was miles per minute faster. Janet's overall time would have been minutes faster had she ridden her bike the whole race at the faster pace.

TO FIND: What was Janet's average speed (in miles per minute) for the whole race?

SOLUTION:

let the speed of Janet in first  

speed of Janet's bike in last  

total time taken by Janet,

Time taken if Janet rides whole race at faster pace

As, Janet's overall time would have been faster had she ridden her bike the whole race at the faster pace.

on solving we get

Average speed

Average speed

Therefore average speed of Janet was

10000

step-by-step explanation: divide by 2,