SOLUTION: please help me solve this problem: Ivanna can jog to work in 3/4 of an hour. When she rides her bike, it takes her 1/3 of an hour. If she rides miles 9 per hour faster than she jog
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Question 433161: please help me solve this problem: Ivanna can jog to work in 3/4 of an hour. When she rides her bike, it takes her 1/3 of an hour. If she rides miles 9 per hour faster than she jogs, how far away is her work? Found 2 solutions by stanbon, katealdridge:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Ivanna can jog to work in 3/4 of an hour. When she rides her bike, it takes her 1/3 of an hour. If she rides miles 9 per hour faster than she jogs, how far away is her work?
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Jogging DATA:
time = 3/4 hr; rate = x mph ; distance = rt = (3/4)x miles
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Riding DATA:
time = 1/3 hr; rate = x+9 mph ; distance = rt = (1/3)(x+9) miles
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Equation:
distance = distance
(3/4)x = (1/3)(x+9)
Multiply both sides by 12 to get:
9x = 4x+36
5x = 36
x = 36/5 = 7 1/5 miles (distance to work)
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Cheers,
Stan H.
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You can put this solution on YOUR website! I hate problems like this.
Okay, d=rt (distance = rate*time)
let =the rate of jogging to work
let =the rate of biking to work
so is the rate equation for jogging to work
and is the rate equation for biking to work
d is the same for both equations because there is only 1 distance to work.
But they also tell you that she rides 9 miles/hr faster than she jogs. This means:
So you can now take the biking equation and substitute in for the new biking equation
Now take both equations, the new biking and the jogging, and set them equal to each other: Now solve for Simplifying a little distributing the subtracting from both sides. multiplying both sides by
This means the rate of jogging to work is 7.2 miles/hour (sounds more like sprinting to me)
Now that you've got that done, you can find out the distance. plug in 7.2 for
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