Time, Speed and Distance Question 3 - CAT 2020
Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-third of her usual total time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is:
Step-by-Step Explanation
Find the total distance (D) and usual time (T):
D/35 − D/40 = 6 minutes = 6/60 = 1/10 hour
(8D − 7D)/280 = 1/10 ⟹ D = 28 km
Usual Time (T) = 28 km/40 km/hr = 0.7 hours = 42 minutes
Track the special journey day:
She covers 2/3 of her total distance in 1/3 of her total time:
Distance covered = 2/3 × 28 = 56/3 km
Time spent = 1/3 × 42 = 14 minutes
She then stops for an 8-minute break. Total time elapsed so far = 14 + 8 = 22 minutes.
Calculate the required speed for the remaining stretch:
Remaining Distance = 28 − 56/3 = 28/3 km
Remaining Time = 42 − 22 = 20 minutes = 1/3 hour
Required Speed = (28/3 km)/(1/3 hour) = 28 km/hr
Correct Option: C
💡 FundaMakers Tip:
Use the inverse ratio of speeds to find the usual time without variables. The speed ratio is 40 : 35 = 8 : 7, meaning the time taken ratio is 7 : 8. The difference of 1 part corresponds to the 6-minute delay, so her standard schedule time is 7 × 6 = 42 minutes. Once you have this baseline, the rest of the problem becomes a simple checklist of remaining distance and remaining time.