Question

Amit drives a car daily to his office from his home. The distance is 24km. On a particular day, he left his home at 8 :15 AM, drove for 5km at a speed of 60kmph. After that he was stuck in a traffic jam of 1km during this stretch he could drive only at a speed of 15kmph.
Which of these is the closest to the minimum speed at which he should drive after the traffic jam to ensure that he reaches the office by 8:45 AM? ( Assuming that he can drive the way he wants to, without any traffic jams)

Answer 1

Given:

Distance of office

case-1:

Amit drove 5 km at 60 kmph

case-2:

He was struck in traffic of 1 km at a speed of 15 kmph

Solution:

We have $Speed=\frac{Distance}{Time}$

CASE-1:

speed=60×5/18  m/s = 50/3 m/s

distance=5000 m

so, $\frac{50}{3} =\frac{5000}{time}$

time=300 seconds = 5 minutes

So he travelled 5 km distance in 5 minutes i.e., by 8:20 AM

CASE-2:

speed=15×5/18 =25/6 m/s

distance = 1000m

so,  $\frac{25}{6} =\frac{1000}{time}$

time = 240 seconds = 4 minutes

So now by 8:24 AM he travelled a distance of 6 km

Now the distance to be travelled = (24-6)km = 18 km= 18000 m

And time left = 21 minutes = 1260 seconds

Now , $Speed=\frac{18000}{1260}$

         Speed = 14.28 m/s

         Speed = 14.28 × 18/5  kmph

         Speed = 51.42 kmph

Here after traffic jam Amit has to drive with a minimum speed of 51.42 kmph

So 60kmph is closest to the minimum speed he should drive after the traffic jam.