GRE® Quant Practice | Rates Q2

The GRE maths sample question given below is a time and speed question from Rates. This GRE sample question helps you understand the concept of computing Average Speed.

Question 2: Sam covers the first 40% of the distance between two cities A and B at 50 kmph and the remaining distance at a speed of 75 kmph. What is his average speed for the entire travel?

1. 62.5 kmph
2. 65 kmph
3. 60 kmph
4. 66.66 kmph
5. 58.33 kmph

---

---

Video Explanation

---

---

Explanatory Answer | GRE Time Speed Distance Q2

Given Data: Speeds for the first and the second part of journey

Speed for the first 40% of the distance = 50 kmph
Speed for the remaining 60% of the distance = 75 kmph

Average Speed Formula
Average Speed = \\frac{\text{Total Distance}}{\text{Total Speed}})

What is the total distance ?
The question stem has not provided the total distance of travel.
The quickest way to solve the question is to assume a value for the distance.
To compute the time taken we will divide the distance by speed.
So, it makes sense to assume such a value for distance that is divisible by both 50 and 75 so that the results will be integers.

So, the value that we assume for distance should be a multiple of 50 and a multiple of 75.
i.e., it should be a common multiple of 50 and 75.
The smallest common multiple is the LCM of (50, 75).
LCM (50, 75) = 150

Let 40% of the distance be 150 km.
∴ 60% of the distance = \\frac{60}{40}) × 150 = \\frac{30}{2}) × 150 = 225 km

Part	Speed	Distance	Time Taken
First 40%	50 kmph	150 km	\\frac{150}{50}) = 3 hours
Remaining 60%	75 kmph	225 km	\\frac{225}{75}) = 3 hours
Total		375 km	6 hours

Average Speed = \\frac{375}{6}) = 62.5 kmph

Choice A is the correct answer