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 hr
- 90 min
- 3 hrs
- 150 min
- 4.5 hrs

From INR 2999

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.

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**

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.

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