Distance, combined labor

[nrhovis]

I'm not sure if this is a shared labor problem or not. No matter how I set it up, it doesn't work out.
Janet jogged 10 miles then cycled 45.5 miles. She finished both in a total of 4.5 hours. She cycled 6 mph faster than she jogged. What was her rate when cycling?

 

[stapel]

I'm not sure if this is a shared labor problem or not. No matter how I set it up, it doesn't work out.

Please reply showing your set-up.

Janet jogged 10 miles then cycled 45.5 miles. She finished both in a total of 4.5 hours. She cycled 6 mph faster than she jogged. What was her rate when cycling?

To learn the general process for setting up this sort of exercise, please try (here). Using the method explained there:

. . .jogging:
. . . . .rate: r
. . . . .time: t
. . . . .distance: 10 = rt

. . .cycling:
. . . . .rate: [create expression, in terms of "r", for this rate]
. . . . .time: [create expression, in terms of "t", for the amount of the 4.5 hours left after she'd jogged]
. . . . .distance: 45.5

Solve the first equation for one of the variables in terms of the other; say, solve for t = 10/r. Then plug this into the second equation, and solve for the variable. If you use "t = 10/r", then you'll be solving for the value of r. At some point, you may find it useful to multiply through on both sides by "r", in order to get the variable out of the denominator (and also, if you prefer, by 2, in order to get rid of the decimals; and then divide by 3, to make the coefficients smaller).

Apply the Quadratic Formula (here) to the result. Remember that only one of those solutions will make sense within the context of somebody travelling forward.

 

[nrhovis]

Distance, Rate problem

I had already tried several times using the method you recommended. No matter what I do I cannot get to the solution which is 14 mph.

 

[stapel]

I had already tried several times using the method you recommended. No matter what I do I cannot get to the solution which is 14 mph.

In order for us to check your work, we'll first need to see it. So kindly please reply with a clear listing of your efforts so far. Thank you!

 

[stapel]

Whadda heck is a "shared labor problem"

Here's an example: "Linda can finish washing up after Thanksgiving dinner in forty-five minutes. Bill, who is trying to convince Linda never to ask him again to help, manages to stretch the task to three hours. How long would it take if they worked together?"

 

[nrhovis]

Distance, Rate problem

In order for us to check your work, we'll first need to see it. So kindly please reply with a clear listing of your efforts so far. Thank you!

I was going to scan and attach my work then spotted a simple math error at the end of my calculations. I finally calculated the correct answer! Thanks for your help! :grin: