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How do start the equation

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KB began a 186-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, the bicycle chain broke, so he finished the trip walking. The whole trip took 6 hrs. If KB walks at a rate of 4 mph and rides at 40 mph, find the amt of time he spent on his bicycle. Thank you for your assistance.

Math58  Dec 1, 2014

#2
+92596
+5

Here's another way to do this without simultaneous equations.....

Call the time on the bicycle "x".....then the time walking was (6-x)

And....rate times time = distance

So the amount of time on the bike times its rate plus the amount of time walking times that rate = total distance.

40x + 4(6-x)  = 186

40x + 24 - 4x = 186   simplify

36x = 162      divide both sides by 36

x = 4 + 1/2 hrs = 4 hrs 30 minutes

And that's the time on the bike

CPhill  Dec 1, 2014
#1
+94101
+5

Let B be the distance ridden and let W be the distance walked.

$$B+W=186 \quad(1)$$

now   speed=distance/time

so      time = distance/speed

Time for the bike ride = B/40

Time for walking = W/4

$$\frac{B}{40}+\frac{W}{4}=6$$

multiply both sides by 40 and we have

$$B+10W=240\quad (2)$$

Melody  Dec 1, 2014
#2
+92596
+5

Here's another way to do this without simultaneous equations.....

Call the time on the bicycle "x".....then the time walking was (6-x)

And....rate times time = distance

So the amount of time on the bike times its rate plus the amount of time walking times that rate = total distance.

40x + 4(6-x)  = 186

40x + 24 - 4x = 186   simplify

36x = 162      divide both sides by 36

x = 4 + 1/2 hrs = 4 hrs 30 minutes

And that's the time on the bike

CPhill  Dec 1, 2014