Who can solve this math problem?

[falias]

Can anyone explain to me how to solve this? Thanks.

Tom can ride his bike 15 mph faster than he can run. If he finished a biathlon (6 mile run, 15 mile bike, 3 mile run) in 1.5 hours, how fast can he ride the bike?

All I know is t = d/r

 

[Rallispec]

x is the speed of running

6x + 15(x+15) + 3x = 1.5 hours.

solve for x.


i think.


edit to fix numbers

 

[falias]

ya, didn't work, it turned out to be -9 point something....thanks for trying. Anyone else?

 

[ErmanC]

Close but not quite. If its too detailed forgive me, but here's the answer....

if X = running speed = distance / time

then bike speed = (X+15)

time = distance / speed

then for a biathlon
total time = (6 / X) + (15 / (X+15)) + (3 / X) = 1.5 hours


Here's the algebra....

multiply through by X
6 + (15 X / (X+15)) + 3 = 1.5 X

multiply through by (X+15)
6 (X+15) + 15 X + 3 (X+15) = 1.5 (X) (X+15)

expanding
6X + 90 + 15 X + 3X + 45 = 1.5 (X^2 + 15X)
6X + 90 + 15 X + 3X + 45 = 1.5X^2 + 22.5X

collecting terms
1.5X^2 -1.5X - 135 = 0

divide through by 1.5
X^2 - X - 90 = 0

factoring
(X+9)(X-10) = 0
so X = -9 or X = 10

since you can't run a negative speed, then X (his running speed) must equal 10 mph
and thus his biking speed = X + 15 = 25 mph

 

[falias]

Cool, props to ErmanC, Thanks

 

[ErmanC]

No problem, glad to help.