SOLUTION: Ok, Its been years for me and so here is the questions I have. I know that distance = time * rate. But here is my question, I'm not sure how to set this one up. Alexandra live

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Question 24153: Ok, Its been years for me and so here is the questions I have. I know that distance = time * rate. But here is my question, I'm not sure how to set this one up.
Alexandra lives thirty-three miles from work. During the summer, she rides her bike at seven mph to the metro station. She then takes the metro to work, which travels at thirty-nine mph. If she spends twenty-one minutes (which is .35 hour) less on the bike than on the metro, what is the distance from her house to the metro? (Work with the time in hours and round the final answer to a whole number.) If you could please Help me thanks Mari
Answer by kev82(151) (Show Source):
You can put this solution on YOUR website!

You've got the right equation, which is always a good start :) If you're not sure what to do next then the best thing to do is write down everything you know. Let's try that. First, the thing we want to know is the distance from house to metro, we'll call this .

The first useful piece of information is that work is 33 miles away, from this we know that plus the distance from metro to work is 33. Or as an equation:

Next we are told about the travel speeds, from which we can work out the travel times. She rides the bike at 7 mph so . Similarly she rides the metro at 39 mph so

Finally we know the difference between the times is 0.35, so . If you look back on what we've done, you should notice we have four equations, and four variables, which is solvable. Hopefully you can do the rest now.

I think the answer comes out at a little above 7. If you have any problems or didn't follow what I did then plaese write back.

Hope that helps.

Kev