Question

Andrew travels a distance of 100 km in the following manner - at 20 km/h for the first 50 km
and at 25 km/h for the next 50 km; he returns at a constant speed of 25 km/h. What was his
average speed for the journey?​

Answer 1

Step-by-step explanation:

avg. speed = total distance covered/ total time

Now total distance is 200km including returning

and

time taken in 1st 50km [t(1)] = distance/ speed

t(1) = 50 / 20

t(1) = 2.5 hr

time taken in 2nd 50 km [t(2)] = distance/ speed

t(2) = 50 / 25

t(2) = 2 hr

time taken in returning 100km [t(3)] = distance/ speed

t(3) = 100/ 25

t(3) = 4 hr

Now total time = 2.5 + 2 + 4 => 8.5 hr

total distance = 200 km

avg. speed = 200 / 8.5

avg. speed = 23.52 km/hr

Answer 2

Given,

Speed for 50 km $\[ = 20km/h\]$

Speed for next 50 km $\[ = 25km/h\]$

Speed in returning $\[ = 25km/h\]$

Solution,

Know that,

$\[{\rm{time = }}\frac{{{\rm{distance}}}}{{{\rm{speed}}}}\]$

$\[{\rm{ = }}\frac{{100 + 100}}{{\frac{{50}}{{20}} + \frac{{50}}{{25}} + \frac{{100}}{{25}}}}\]$

$\[{\rm{ = }}\frac{{200}}{{2.5 + 2 + 4}}\]$

$\[{\rm{ = }}\frac{{200}}{{8.5}}\]$

$\[{\rm{ = }}23.53\,km/h\]$

Hence the average speed for the journey is $\[{\rm{ }}23.53\,km/h\]$