Question

Alice leaves her house, driving east at 45 miles per hour (mph). 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 with Alice 3 hours after he leaves?

explain please :))))))))))))))

Answer 1

Is there any missing info such as the speed of the husband?

Answer 2

no, thats all what it says :/ @seraphic_topaz

Answer 3

Because she travels at the speed of 45 mph, in 30 min she must have been 45 mph x .5 hr = 45/2 miles away from her house. The husband must go through this distance, and then...

00ps, my bad. The question asks How fast...not How far... Sorry!

Answer 4

Anyway, Dave must go thru 45/2 miles and then travels faster than Alice during each hour in order to catch up with her.

***Example: Dave's speed = 55 mph ==> each hour he'll travel 10 miles more than Alice;
if Dave's speed = 75 mph ==> each hour he'll travel 30 miles more than Alice.

Now, after going thru 45/2 miles, lets say Dave and Alice are 60 miles apart, then Dave must travel at 65 mph to catch up with her in 3 hours (65 - 45 = 20; 60/3 = 20).

Answer 5

If you're with me, then we'll add another level of complexity.

The question is "How fast must Dave travel in order to catch up with Alice **3 hours after he leaves**?" That means in 3 hrs he must go thru 45/2 miles and then go faster than Alice in each hour until they meet.

30 min after Alice left the house, Dave left the house. Now 3 hrs after Dave left, how far is Alice from the house?

30 min + 3 hrs = 3.5 hrs

Alice's speed is 45 mph ==> She is 45 x 3.5 = ?? miles from the house.

Dave must go through ?? miles to meet Alice in 3 hrs, then his speed must be:
??/3 = ??? mph

Answer 6

alice is 157.5 miles from the house...dave must go 49mph? idk @seraphic_topaz

Answer 7

You got the first one, then 157.5/3 = 52.5 right?

Answer 8

yup thank u very much