## 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__

__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__

__To Find__

We need to determine

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

__Approach & Working__

__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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