SOLUTION: while training for a duathlon, you run and bike a total of 23 kilometers in 1.25 hours. You run at an average speed of 10 kilometers per hour and bike at an average speed of 24 kil

Question 1170962: while training for a duathlon, you run and bike a total of 23 kilometers in 1.25 hours. You run at an average speed of 10 kilometers per hour and bike at an average speed of 24 kilometers per hour. Write and solve an equation to find the time you spend running and the time you spend biking.

Found 3 solutions by Theo, MathTherapy, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the general formula is rate * time = distance.

for the bike, this formula becomes 24 * t1 = d1 *** first original equation.
for the running, this formula becomes 10 * t2 = d2 *** second original equation.

you are given that t1 + t2 = 1.25 hours.
you are given that d1 + d2 = 23 kilometers.

solve for t1 to get t1 = 1.25 - t2.
solve for d1 to get d1 = 23 - d2.

the formulas for the bike and the running become:

24 * (1.25 - t2) = 23 - d2
10 * t2 = d2

simplify these equations to get:

30 - 24 * t2 = 23 - d2 *** first simplified equation.
10 * t2 = d2 *** second simplified equation.

solve for t2 in the second simplified equation to get:

t2 = d2 / 10

replace t2 in the first simplified equation to get:

30 - 24 * d2 / 10 = 23 - d2

simplify to get:

30 - 2.4 * d2 = 23 - d2

add 2.4 * d2 to both sides of this equation and subtract 23 from both sides of this equation to get:

30 - 23 = 2.4 * d2 - d2

combine like terms to get:

7 = 1.4 * d2

solve for d2 to get:

d2 = 7 / 1.4 = 5

since d1 + d2 = 23, then d1 must be equal to 23 - 5 = 18.

you have:

d1 = 18 kilometers.
d2 = 5 kilometers.

go back to both original equations and replace d1 and d2 with their respective values to get:

24 * t1 = d1 becomes 24 * t1 = 18
10 * t2 = d2 becomes 10 * t2 = 5

solve for t1 and t2 to get:

t1 = 18/24 = .75 hours.
t2 = 5/10 = .5 hours.

t1 + t2 = 1.25 hours.
this is what it's supposed to be, confirming the distances were calculated correctly.

.75 hours * 24 kilometers per hour = 18 kilometers.
.5 hours * 10 kilometers per hour = 5 kilometers.

18 + 5 = 23 kilometers.
this is what it's supposed to be, confirming the times were calculated correctly.

yout solution is that the time spent running is .5 hours and the time spent biking is .75 hours.
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

while training for a duathlon, you run and bike a total of 23 kilometers in 1.25 hours. You run at an average speed of 10 kilometers per hour and bike at an average speed of 24 kilometers per hour. Write and solve an equation to find the time you spend running and the time you spend biking.

You're NOT asked to find the distance, so finding the distance is TOTALLY UNNECESSARY, as the other person did!
Let the time spent running be T
Then the time spent biking = 1.25 - T
We then get the following DISTANCE equation: 10T + 24(1.25 - T) = 23
10T + 30 - 24T = 23
10T - 24T = 23 - 30
- 14T = - 7
Time spent running. or
Time spent biking:
That's ALL to this problem! Nothing COMPLEX about it!!
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!

SPEED TIME DISTANCE RUN 10 x 10x BIKE 24 1.25-x 24(1.25-x) Total 1.25 23

-----------time bicycling, in hours

---------time in hours, running
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