Question 148319
You can walk 10 miles in the same time that it takes to travel 15 miles by bicycle. If the bike's rate is 3 miles per hour faster than your walking rate, find the average rate for each.
:
Let x = walking rate
then
(x+3) = biking rate
:
Write a time equation: Time = {{{dist/rate}}}
:
Biking time = walking time
{{{15/((x+3))}}} = {{{10/x}}}
Cross multiply
:
15x = 10(x+3)
:
15x = 10x + 30
:
15x - 10x = 30
:
5x = 30
x = {{{30/5}}}
x = 6 mph, that's really fast walking!
then
6 + 3 = 9 mph is the bike rate
:
:
Check solution by finding the time for each:
15/9 = 1.67 hrs
10/6 = 1/67 hrs; confirm our solutions