Thread: Help changing word problem into an equation please

Could someone help me to understand how to form an equation that will solve the following problem please?

Harry and Sally live 21 miles apart. One day they leave their houses at noon. Harry walks towards Sally's at 4mph and Sally cycles towards Harry's at 10mph. At what time do they meet?

Thanks ~ Marilyn

Originally Posted by Meggomumsie

Harry and Sally live 21 miles apart. One day they leave their houses at noon. Harry walks towards Sally's at 4mph and Sally cycles towards Harry's at 10mph. At what time do they meet?

To learn, in general, how to set up and solve this sort of exercise, try here.

Note that Harry and Sally are covering the 21 miles by approaching each other from opposite ends of this distance. So their individual distances will be additive.

If Harry's rate is r = 4 and he covers "x" of the 21 miles, then, using "d = rt" in the form "d/r = t", what is the expression for the distance that he covers?

Since Harry has covered "x" of the 21 miles, then how many miles are left for Sally to cover? If she covers this distance at a rate of r = 10, then what is the expression for her distance?

Add the two "distance" expressions, and set equal to the given total. Then solve the resulting linear equation for the value of "x". Back-solve to find the time taken to cover those "x" miles.

If you get stuck, please reply showing your steps and reasoning so far, so we can see where you're having trouble. Thank you!

Originally Posted by stapel

To learn, in general, how to set up and solve this sort of exercise, try here.

Note that Harry and Sally are covering the 21 miles by approaching each other from opposite ends of this distance. So their individual distances will be additive.

If Harry's rate is r = 4 and he covers "x" of the 21 miles, then, using "d = rt" in the form "d/r = t", what is the expression for the distance that he covers?

Since Harry has covered "x" of the 21 miles, then how many miles are left for Sally to cover? If she covers this distance at a rate of r = 10, then what is the expression for her distance?

Add the two "distance" expressions, and set equal to the given total. Then solve the resulting linear equation for the value of "x". Back-solve to find the time taken to cover those "x" miles.

If you get stuck, please reply showing your steps and reasoning so far, so we can see where you're having trouble. Thank you!

Thanks for the link and the help so far. I still haven't got it yet. I could do this type of problem in a kind of remote way but I am trying to achieve understanding of what I am doing and why.

The expression for the distance covered by Harry will be 21/4=t
The expression for the distance covered by Sally will be 21/10=t

Now I'm lost because after using the link you gave me, I know I can get the answer from 21=4t+10t
21/14= t
t= 1hour 30 minutes which I know from the book is the correct answer.

However, I would like to understand what you meant by 'Add the two "distance" expressions, and set equal to the given total'. I probably am missing something here. If I add the two 'distance' expressions, I get 42/14 = t

No, that's not right I think I am now mixing the two different ways of approaching the problem and I am really lost.

Unless each walked the entire distance, then their distances should not be "21", but instead the "x" and "21 - x" suggested earlier.

Since the two times will be the same, correct the "time" expressions (not "distance", as I erroneously typed earlier) and set them equal. Solve for "x", and then back-solve for the requested value.

Originally Posted by Meggomumsie

Could someone help me to understand how to form an equation that will solve the following problem please?

Harry and Sally live 21 miles apart. One day they leave their houses at noon. Harry walks towards Sally's at 4mph and Sally cycles towards Harry's at 10mph. At what time do they meet?

Thanks ~ Marilyn

I like to use a relative velocity approach for these sorts of problems:

Assume that Harry doesn't move and Sally cycles towards Harry at 14 mph. It takes Sally 21/14 = 3/2 hours to get to Harry. So they meet after 3/2 hours.