SOLUTION: Some time ago, you asked the following problem: ``Oscar finished the 44 km trip in 6 hours. He traveled part of the distance at 4km/h and part at 9 km/h. How long did he travel

Question 1071145: Some time ago, you asked the following problem:
``Oscar finished the 44 km trip in 6 hours. He traveled part of the distance at 4km/h and part at 9 km/h. How long did he travel at 9 km/h?
A. 2 hours
B. 4.9 hours
C. 5 hours
D. 4 hours

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = distance.

let d1 and d2 = distances involved.
let t1 and t2 = times involved.

you will get 2 equations.

4 * t1 = d1
9 * t2 = d2

you know that d1 + d2 = 44 and you know that t1 + t2 = 6
solve for d2 to get d2 = 44 - d1
solve for t2 to get t2 = 6 - t1

your equations will become:

4 * t1 = d1
9 * (6 - t1) = 44 - d1

since d1 = 4 * t1 from the first equation, replace d1 in the second equation with 4 * t1 to get:

9 * (6 - t1) = 44 - 4 * t1

simplify to get 54 - 9 * t1 = 44 - 4 * t1

subtract 44 from both sides of the equation and add 9 * t1 to both sides of the equation to get 54 - 44 = 9 * t1 - 4 * t1

simplify to get 10 = 5 * t1

solve for t1 to get t1 = 2.

since t1 + t2 = 6, then t2 = 4.

go back to your original equations of:

4 * t1 = d1
9 * t2 = d2

replace t1 with 2 and t2 with 4 to get:

4 * 2 = d1
9 * 4 = d2

solve for d1 to get d1 = 8

solve for d2 to get d2 = 36

he traveled 2 hours at 4 kmph for a distance of 8 km.
he traveled 4 hours at 9 kmph for a distance of 36 km.

your solution is that he traveled for 4 hours at 9 kmph.

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

Some time ago, you asked the following problem:
``Oscar finished the 44 km trip in 6 hours. He traveled part of the distance at 4km/h and part at 9 km/h. How long did he travel at 9 km/h?
A. 2 hours
B. 4.9 hours
C. 5 hours
D. 4 hours

Let time taken on 9 km/h-leg, be T
Then we get the following DISTANCE equation: 9T + 4(6 - T) = 44
Solve for T, the time taken on the 9 km/h-leg.
It's that simple.....nothing complex!
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