Dear Reader, Below are three questions based on speed, time and distance.

Question 1

Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?

(a)15 hours (b)10 hours (c) 50 hours (d)25 hours

Answer : b)10 hours

Solution:

Since Raina and Gambhir are travelling in opposite directions, Gambhir's Relative speed with respect to Raina's = Speed of Raina + Speed of Gambhir = 6 + 6 = 12 miles per hour.
Now housefly starts from Raina's cycle and travels towards Gambhir's cycle at 17 miles per hour.
Relative speed of housefly with respect to Gambhir = Speed of housefly with respect to Raina - Speed of Gambhir with respect to Raina = 17 - 12 = 5 miles per hour
Time taken for housefly to reach Gambhir = Distance to catch up / Relative speed of housefly with respect to Gambhir = 50/5 = 10 hours.

Question 2

Pinky and Ponky decided to have a car race. Initially Pinky was 20 miles behind Ponky’s car. Both of them took the race in the same direction along the same route. Pinky was travelling at a constant speed of 68 miles per hour, while Ponky was travelling at a constant speed of 60 miles per hour. How many hours will it take for Pinky to overtake and drive 8 miles ahead of Ponky?

(a)1.7 hours (b)2.0 hours (c)2.5 hours (d)3.0 hours (e) 3.5 hours

Answer : e) 3.5 hours

Solution:

It is to be understood from the problem, that Pinky has to travel 20 miles first to catch up Ponky. Then, he has to travel an additional 8 miles to be ahead of Ponky. Pinky has to travel a total of 28 extra miles relative to Ponky’s car.
Relative Speed of Pinky with respect to Ponky = 68 - 60 = 8 miles per hour.
Time taken for Pinky to cover 28 extra miles compared to that of Ponky = Extra Distance / Relative Speed of Pinky with respect to Ponky = 28/8 = 3.5 hours.

Question 3

Eveson was working for a multinational company. The pressure of work in the company was too heavy due to seasonal sales. Eveson decided to go weekend trip with his wife for relaxation. Husband and wife decided that the proposed trip should not exceed 8 hours driving in a day. They decided to maintain the average Speed of forward journey to 40 mph. Due to traffic on Sundays the return journey average speed can only be at 30 mph. How far the couple can select a picnic spot?

(a)142 Miles (b)200 Miles (c)137 Miles (d)220 Miles

Answer : c)137 Miles

Solution:

If x and y are the speeds corresponding to forward and return journeys, then average speed of the entire journey can be found using the formula : 2xy / x+y
In our case the rate for onward journey is given as 40 mph and rate for return journey is given as 30 mph
Hence average speed = 2x40x30 / 40+30 = 2400 / 70 = 240 / 7 mph
Total Travel Time is 8 hours. So total distance the couple can plan = Average Speed x Affordable Total Time = 240 / 7 x 8 =1920 / 7 = 274 miles (approximately)
Since 274 miles should be the total distance that can be covered including forward and return journeys, the picnic spot has to be at 274 / 2 = 137 miles approximately.

Question 4

Rambabu is driving a Honda Unicorn Power bike at 80 km per hour. However being sugar patient, Rambabu could not travel continuously. He takes small breaks each of 2 minutes for every 15 minute of his drive. How much distance Rambabu will cover in 90 minutes?

a)118Km b)89Km c)112Km d) 104km

Answer : d) 104km

Solution:

For every 15 minutes he takes a rest for 2 minute.
Hence for 90 minutes of drive he would require 12 minutes of rest. In effect he will be traveling for 90 - 12 = 78 minutes.
For 60 minutes he covers 80 Km.
For 1 minute he would cover 80/60 Km.
For 78 minutes he would cover (80/60)78 = 104 Km