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In 30 min she would have traveled 22.5 miles so if you wanted to catch up to her in 30 min you would have to travel twice her hourly rate which would be 90 miles per hour

Dave will catch Alice if he travels at any speed greater than she does, that is if he drives at any speed greater than 45mph.

The factor which changes is the time it takes Dave to catch Alice (assuming they both keep driving at their relevant speeds):

at 46mph, he will take 22.5/1 = 22 1/2 hours to catch her;

at 55mph, he will take 22.5/10 = 2 1/4 hours to catch her;

at 70mph, he will take 22.5/25 = 54 minutes to catch her.

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Q: Alice leaves her house driving east at 45 miles per hour Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her How fast must Dave travel in order to catch up?
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