MHB How Do Jane and Terry Divide 10.35 Miles of Treadmill Exercise in 3.5 Hours?

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Jane and Terry walked a combined distance of 10.35 miles on treadmills over 3.5 hours, with Jane walking at 4.9 miles per hour and Terry at 4.5 miles per hour. The problem involves setting up equations based on their rates and times, where Jane's distance can be expressed as d_J = 4.9t_J and Terry's as d_T = 4.5t_T. The total distance and time constraints lead to the equations d_J + d_T = 10.35 and t_J + t_T = 3.5. Participants in the discussion suggest using these equations to solve for the time each person spent on their treadmill. The conversation emphasizes the need for clarity in the problem setup to proceed with the calculations effectively.
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This problem has me stumped

Jane and Terry used two different treadmills to exercise. The total distance waled between them was 10.35 miles. Jane waled at a pace of 4.9 per hour and Terry walked the pace of 4.5 per hour. Their total time as 3.5 hours.

This is how I would set it up, but not sure if it is correct

Jane - Rate = x, Time = 1, Distance = 4.9
Terry - Rate = x, time = 1, Distance = 4.5

After this - if this set-up is correct - I get lost in what to do next...
 
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I am also lost as to what to do next, because there is no question mark in your post... can you post the entire problem?
 
Bacterius said:
I am also lost as to what to do next, because there is no question mark in your post... can you post the entire problem?

Sorry - The question is : How long did each person spend on their treadmill?
 
Distances are in miles and time is in hours.

For Jane we have:

$$d_J=4.9t_J$$

And for Terry we have:

$$d_T=4.5t_T$$

We are also given:

$$d_J+d_T=10.35$$

$$t_J+t_T=3.5$$

You can use the latter two equations to express both of the first two equations in terms of one person. At this point you will have two equations and two unknowns...can you proceed?
 
Thank you
 
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