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?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Word Problems |
| Sub-Topic | Distance |
| Difficulty | Medium |
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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