Question

A commuter drives 10 miles on first day at a speed of 60km/hr , second day at 15 km/hr and third day 10km/hr. The mean speed of the commuter is

Answer 1

Given:

A commuter drives 10 miles on the first day at a speed of 60km/hr, the second day at 15 km/hr and the third day 10km/hr. The mean speed of the commuter is?

To find:

The mean speed of the commuter

Solution:

The distance travelled by the commuter for each trip = 10 miles ≈ 16 km . . . [∵ 1 mile ≈ 1.6 km]

We know,

$\boxed{\bold{Time = \frac{Distance }{Speed} }}$

So, the time spent on each trip by the commuter:

1st trip → $\frac{16\:}{60\:km/hr} = \frac{4}{15}\:hr$

2nd trip → $\frac{16\:km}{15\:km/hr} = \frac{16}{15}\:hr$

3rd trip → $\frac{16\:km}{10\:km/hr} = \frac{8}{5}\:hr$

The total distance travelled by the commuter = 16 + 16 + 16 = 48 km

We know,

$\boxed{\bold{Avearge \:speed = \frac{Total \:distance }{Total \:time } }}$

Now, based on the above formula, we get

The average speed of the commuter is,

= $\frac{48}{\frac{4}{15} + \frac{16}{15} + \frac{8}{5} }$

= $\frac{48}{\frac{4\: +\: 16 \:+ \:24}{15} }$

= $\frac{48\times 15}{4\: +\: 16 \:+ \:24} }$

= $\frac{720}{44}$

= $\bold{16.36\:km/hr}$

Thus, the mean speed of the commuter is → 16.36 km/hr.

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