Dear Reader, Below are three simple problems on rate and time.

Question 1

An Air France jet flight from the City of Chicago to Bentenwel started its journey at 9.00AM from Chicago domestic air port. Another flight Airway International started from Chicago to Bentenwel at 10.00AM (exactly one hour later), Airway International was within the minimum separation distance, following Air France jet at 12.00 noon.What is the average speed of Air France jet?

(a)740 kmph (b) 450kmph (c) 370 kmph (d) 430 kmph

Answer : c) 370 kmph

Solution:

Let us use the basic formula Distance = time x rate.
Assume the speed of Air France be X kmph. Air France has travelled for three hours till 12 PM when both the flights are at minimum separation. Similarly until minimum separation distance, Rate and time taken by Airway International are 555 kmph and 2 hours.

(Note: Minimum separation does not mean both the planes are on same air route. They could be in parallel routes. Since no further details are given on air routes by the planes, the only way to solve is to assume that the distance travelled by both planes during minimum separation is same.)

Based on above note, we can equate the distance travelled by Air France in 3 hours to that of Airway International in 2 hours.
3 * X = 555 x 2 or
3X = 1110 and
X = 370 kmph.

Question 2

The famous Denali Star train starts from Anchorage and travels towards Fair Banks at a speed of 50 mph. After some time, another train Glacier Discovery starts (from a parallel track to the Denali Star train) at Fair Banks and moves towards Anchorage at a speed of 70 mph. Both the trains Denali Star and Glacier Discovery have a length of 1/6 miles each. After the trains meet, how many seconds will the faster train take to overtake the slower one?

(a) 60 seconds (b) 20 seconds (c) 180 seconds (d) 32 seconds

Answer : a) 60 seconds

Solution:

Relative speed of faster train with respect to that of slower train = 70 - 50 = 20 mph
After the trains meet the faster train has to cross the entire length of the slower train as well as its own length to overtake the slower train.

Distance to be covered by faster train while overtaking = 1/6 + 1/6 = 1/3 miles
Time taken for overtake = Distance to be covered / Relative speed = 1/3 / 20 = 1/60 hours
Since all the options are given in units of seconds, we can calculate the equivalent number of seconds for 1/60 hours as below

hour    seconds
1        3600
1/60      ?

3600/60 = 60 seconds

Question 3

The Coramandal Express leaves Chennai Central at 7.30 AM and reaches Howrah 6.00AM the next day. Between Chennai and Howrah, there are 15 halts and the total time the train stopped is 90 minutes. If the distance between Chennai and Howrah is 1400 km What is the average speed of Coramandal Express?

(a) 66kmph (b) 72 kmph (c) 70 kmph (d) 88 kmph

Answer : c) 70 kmph

Solution:

Total Time taken by Coramandal Express = 22 1/2 hours (from 7.30AM of the day to 6.00am of next day) .

To calculate actual running time of the train, we have to deduct the time consumed in 15 halts i.e we have to deduct 90 minutes.

Therefore, Total running time = 22 1/2 - 1 1/2 = 20 hours.

Distance between the two cities is given as 1400 km. Speed of Coramandal Express can be found by applying the simple formula,

Speed = Distance / time

Substituting distance and running time values in the above formula we get,

Speed = 1400 / 20 = 70 kmph.