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## OGQR 2020: Question No. 79

If Car A took n hours to travel 2 miles and Car B took m hours to travel 3 miles, which of the following expresses the time it would take Car C, traveling at the average (arithmetic mean) of those rates, to travel 5 miles?

### Solution

#### Given

In this question, we are given

• Car A took n hours to travel 2 miles.
• Car B took m hours to travel 3 miles.
• Car C travels at the average (arithmetic mean) of the travel rates of A and B.

#### To Find

We need to determine

• The time car C would have taken to travel 5 miles.

#### Approach & Working

Travel rate of car A = 2/n miles per hour

Travel rate of car B = 3/m miles per hour

• Average of the rates of car A and car B = ½ (2/n + 3/m ) = (3n +2m) / 2mn
• Therefore, time taken by car C = 5 * 2mn / (3n + 2m) = 10mn / (3n + 2m)

Hence, the correct answer is option A.

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