# Giving the speed, find meeting points of two objects.

Two tortoises named A and B must run a race. A starts with an average speed of 720 feet per hour. Young B knows she runs faster than A, and furthermore has not finished her cabbage.

When she starts, at last, she can see that A has a 70 feet lead but B's speed is 850 feet per hour. How long will it take B to catch A?

Could you just walk me through this?

• Welcome to MSE, I edited your question a little to make it more informative (your tag were odd, so I changed it). Commented Feb 6, 2019 at 20:50
• Thank you @WillM. Commented Feb 6, 2019 at 21:05
• it's a basic programming exercise and i am trying to solve it,. No matter how hard i try i end up nowhere. Which class of math do i need to start practice again? Commented Feb 6, 2019 at 21:08
• Just maneuver on basic skills of logic and you should get it @user6787493. BTW is my answer correct? Commented Feb 6, 2019 at 21:09
• i know the answer and yours is correct :). Commented Feb 6, 2019 at 21:11

Every hour, $$B$$ gains $$A$$ a distance of $$850-720=130$$ feet. Since $$70<130$$, we know that the time it takes for $$B$$ to catch up to $$A$$ is less than an hour.

$$6$$ minutes is $$\frac{1}{10}$$ of an hour. In $$6$$ minutes, $$B$$ gains $$130\cdot\frac{1}{10}=13$$ feet on $$A$$.

$$\frac{70}{13}$$ is the amount of $$6-$$minute increments that it takes for $$A$$ to be caught up by $$B$$.

Thus, the total amount of time for $$B$$ to catch up to $$A$$ is $$\frac{70}{13}\cdot 6=\boxed{\frac{420}{13}}\approx\boxed{32.3076923}$$ minutes.

I may be wrong, as I am very tired and am practicing for the AMC 10. Tell me if I made a mistake lol. And if you want clarification just comment and I will add.

Max0815

Hint. Essentially, when $$B$$ starts moving at $$850$$ feet per hour, $$A$$ is at point $$70.$$ In $$t$$ hours $$B$$ will have moved ??? and $$A$$ will have moved ???. You have to come up with two linear equations of $$t$$ (of the form $$\alpha t + \beta$$) and make them equal to find the time.

• Anyone who downvoted, a reason? Commented Feb 6, 2019 at 21:10
• Downvoted? I don't think your post has votes yet. Probably a glitch? Commented Feb 6, 2019 at 21:11

In problems like this, you always find the catch up speed which is the difference between fastest and the slowest. The speed difference is $$130$$ feet per hour. Now all you need to find is how much time is needed to cover $$70$$ feet.