SOLUTION: Mary runs twice as fast as bob and billy runs at 80% of bob’s pace. What fraction of a mile will billy complete in the same time that mary runs 1/3 of a mile ? express your answer

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Mary runs twice as fast as bob and billy runs at 80% of bob’s pace. What fraction of a mile will billy complete in the same time that mary runs 1/3 of a mile ? express your answer      Log On


   

Question 266535: Mary runs twice as fast as bob and billy runs at 80% of bob’s pace. What fraction of a mile will billy complete in the same time that mary runs 1/3 of a mile ? express your answer as a common fraction
Found 2 solutions by drk, Theo:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is similar to an RTD question. we get
person . . . . . .rate . . . . . . .time . . . . . . distance
mary . . . . . . . .2r . . . . . . . .1/(6r) . . . . . . 1/3 = 0.33333
bob . . . . . . . . .r . . . . . . . .
billy . . . . . . . .(0.8r) . . . . . 1/(6r) . . . . . . 2/15 = 0.13333333
---
Billy runs 2/15 of a mile

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mary runs twice as fast as bob.

billy runs 80% as fast as bob.

this means that bob runs 1/.8 times as fast as billy equals 1.25 times as fast as billy.

if bob runs at 5 miles per hour, then billy runs at 80% * 5 miles per hour = 4 miles per hour.

5 miles per hour equals 1.25 times 4 miles per hour.

now mary runs twice as fast as bob and bob runs 1.25 times as fast as billy.

this means that mary runs 2 * 1.25 = 2.5 times as fast as billy.

so if billy runs at 4 miles per hour, then:

bob runs at 1.25 * 4 = 5 miles per hour, and:

mary runs at 1.25 * 2 * 4 miles per hour equals 10 miles per hour.

10 miles per hour is equals to 2 * 5 miles per hour so the ratios are good.

now if mary runs 1/3 of a mile in T minutes, then:

mary's rate * T minutes = 1/3 mile.

but mary's rate is 2.5 times billy's rate, so the formula becomes:

2.5 * billy's rate * T minutes = 1/3 of a mile.

if we divide both sides of this equation by 2.5, we get:

billy's rate * T minutes = 1/3 mile / 2.5 = 1/7.5 * 2/2 = 2/15 of a mile.

in the same time that mary runs 1/3 of a mile, billy runs 2/15 of a mile.

1/3 * 5/5 = 5/15.

5/15 = 2.5 * 2/15

your answer is billy runs 2/15 of a mile in the same time that mary runs 1/3 of a mile.

now billy runs .8 times as fast as bob, so we have:

billy's rate * T minutes = 2/15 of a mile.

this becomes:

.8 * bob's rate * T minutes = 2/15 of a mile.

divide both sides of this equation by .8 to get:

bob's rate * T minutes = 2/15 of a mile / .8

this means that:

bob's rate * T minutes = 2/12 of a mile.

2/12 of a mile is the same as 1/6 of a mile in T minutes.

1/6 is half of 1/3 confirming that mary runs twice as fast as bob and covers twice the ground as bob.

all measurements check out.

the ratios are good.

the answer should be also be good.

billy runs 2/15 of a mile in the same time that mary runs 1/3 of a mile.