Question: Devi and Mark

Comment on Devi and Mark

Hello Brent, I have a doubt in first approach. I understood till expansion rate of 15 miles/hr. However I'm not clear with how the expansion rate became the shrinking rate and the further calculation of 12/15. Please explain.
greenlight-admin's picture

Since Mark's speed is 15 mph greater than Devi's speed, the gap between them keeps SHRINKING (at a rate of 15 miles per hour) until Mark catches up to Devi (once Mark passes Devi, then the gap between them will start to expand).

By the time Mark starts driving, the GAP between them is 12 miles.

So, to calculate the time until the gap = 0 miles (i.e., Mark catches up to Devi), we need distance/rate

Here, the distance = the initial gap (12 miles)

So, time = (12 miles)/(15 miles per hour)

Does that help?

Cheers,
Brent

using substitution we can solve using below steps.
The distance traveled by Devi for 1 hr is 36 miles so at 2:00 Devi would have traveled 36 miles.
As Mark started 20 mins late, so at 2:00 Mark would have traveled 34 miles. (using cross multiplication Distance traveled for 40 mins = 51*40/60)
So Now we know answer must be greater we can eliminate
A and B and check for other options.
Now for 8 mins Devi would have traveled 4.8 (36*8/60) miles and Mark would have traveled 6.8 miles.(51*8/60)
So 36+4.8 = 34+6.8
and they meet at 2:08 PM
greenlight-admin's picture

That works too!

Would you plz explain how we should calculate 4/5 = 48 ( at minute 2.47) minutes?
thanks
greenlight-admin's picture

We know that the time it takes for Mark to reach Devi = 4/5 hours.
This is the same as saying 4/5 of an hour.
This is the same as saying 4/5 of 60 minutes
4/5 of 60 = (4/5)(60) = 48

Cheers,
Brent

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