Question

A man travelling at 20 kmph arrives at a certain place at 4 p.M. If he travels at 30 kmph, he will arrive at the same place at 2 p.M. At what speed in kmph (approx) must he travel to get there at 3.30 p.M.?

Answer 1

Step-by-step explanation:

Assume x is travelling distance and required speed is v.

given

$\frac{x}{20} - \frac{x}{30} = 2 \\ \frac{x}{20} - \frac{x}{v} \: = \frac{1}{2}$

Eliminate x

$x =2 \times \frac{ 30 \times 20}{30 - 20} = 120kms$

put value of x in second equation

$\: \: \: \: \: \: \: \: \frac{120}{20} - \frac{120}{v} = \frac{1}{2} \\ \\ \implies \frac{120}{v} = \frac{11}{2} \\ \\ \implies v = \frac{240}{11} = 21.81$

Answer 2

The required speed is 34.2 km/hr.

GIVEN

The speed at which man arrives at 4 p.m = 20 kmph.

The speed at which a man arrives at 2 pm = 30 km/h

TO FIND

The speed at which the man should travel to reach 3:30 pm

SOLUTION

We can simply solve the above problem as follows,

Let the speed at which the man should travel be, v km/hr.

And, Distance = x km

The difference once in time = 2 hr

So,

x/30 - x/20 = 2

20x - 30x = 1200

x = 1200/10

= 120 km

Now,

Time is taken to travel 120 km at 30km/hr = 120/30 = 4 hrs

This means that the man started his journey 4 hours before 2 pm ie, at 10 pm

The speed at which the man should travel to reach the place at 3:30 pm = 120/3.5 = 34.2 km/hr

Hence, The required speed is 34.2 km/hr.

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