SOLUTION: Elmo rode his bike for 12 miles and then walked for 6 miles. If the total time of his trip is 2 hours and his bike speed is 10 mph faster than his walking speed, find the speed on
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Question 574623: Elmo rode his bike for 12 miles and then walked for 6 miles. If the total time of his trip is 2 hours and his bike speed is 10 mph faster than his walking speed, find the speed on his bike.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Elmo rode his bike for 12 miles and then walked for 6 miles.
If the total time of his trip is 2 hours and his bike speed is 10 mph faster than his walking speed, find the speed on his bike.
:
let b = the bike speed
then
(b-10) = the walking speed
:
Write a time equation: time = dist/speed
:
bike time + walk time = 2 hrs
+ = 2
multiply by b(b-10)
b(b-10)* + b(b-10)* = 2b(b-10)
cancel the denominators and you have:
12(b-10) + 6b = 2b^2 - 20b
12b - 120 + 6b = 2b^2 - 20b
18b - 120 = 2b^2 - 20b
Combine like terms on the right
0 = 2b^2 - 20b - 18b + 120
2b^2 - 38b + 120 = 0; a quadratic equation
simplify, divide by 2, results
b^2 - 19b + 60 = 0
This factors to
(b-4)(b-15) = 0
Two positive solutions
b = 4, not a reasonable speed
and
b = 15, more like it
:
His bike speed is 15 mph
:
Check this by finding the times (walk speed = 5 mph)
12/15 = .8 hrs
6/5 = 1.2 hrs
---------------
tot time 2 hrs
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