GRE® Quant Practice | Rates Q3

The GRE maths sample question given below is a distance and time question in Rates. This GRE problem solving question will help you understand the relation between speed, distance, and time. A medium difficutly GRE quantitative reasoning practice question.

Question 3: Ron, Sid, and Tom plan to leave city A by 3 cars towards a farmhouse along the same route. Ron travels at 50 mph, Sid at 60 mph. Sid leaves 2 hours after Ron and they reach the farmhouse at the same time. If Tom plans to drive at 80 mph, how long after Sid should Tom leave city A if he wishes to reach the farmhouse at the same time as Ron and Sid?

1. 1 hr
2. 90 min
3. 3 hrs
4. 150 min
5. 4.5 hrs

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Video Explanation

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Explanatory Answer | Time Speed Distance Question 3

Given data

Ron, Sid, and Tom travel along the same route from city A to the farmhouse.
So, the distance travelled by Ron, Sid, and Tom is the same.

Step 1: Equate Distance & Compute Time Taken by Ron and Sid

Let Ron reach the farmhouse in t hours.
Speed at which Ron travelled = 50 mph
So, distance travelled by Ron = 50t ..... (1)

Sid leaves 2 hours later, so Sid travelled (t – 2) hours to cover the same distance.
Speed at which Sid travelled = 60 mph
Distance travelled by Sid = 60(t – 2) ..... (2)

Distance covered by both Ron and Sid is the same. So, equate (1) and (2)
50t = 60(t – 2)
50t = 60t – 120
10t = 120
t = 12 hours
Distance from city A to farmhouse = 50t = 50 × 12 = 600 miles

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Step 2 of solving this GRE Distance & Time Question: Finding when Tom should leave

Tom travels at 80 mph
So, Tom will take \\frac{600}{80}) = 7.5 hours to cover the entire distance.

Sid takes (t – 2) hours = 12 – 2 = 10 hours to travel the distance.
So, Tom should leave 2.5 hours or 150 minutes after Sid did.

Choice D is the correct answer