Question

a man travel to his office with the speed of the 50 km per hour from his home at 9:30 and reach at 10:15 and then returned to his home for lunch at 1 o'clock with speed 30 kilometre per hour find the time he reached home also find his average speed throughout his journey

Answer 1

Hello,

Case 1
Speed of man = 50km/hr

Time taken = 45 mins = 3/4 hrs

Now,
Distance = speed * time
So,.
Distance = 50 *3/4 = 150/4 km

Case 2

Distance =150/4 km

Speed = 30 km/hr

So,
Time = distance /speed

Time =
$\frac{ \frac{150}{4} }{30} = \frac{150}{4 \times 30} = \frac{5}{4} hrs$
Now,.
5/4 *60 = 75 minutes = 1 hour 15 minutes.


Now
He left at 1 o clock
So, he will reach home at 2:15 pm

Now

Total distance traveled = 150/4 km +150/4km
= 300/4 = 75 km

Total time taken =75 + 45 = 120 minutes = 2hrs

So

Average speed = 75/2 = 37.5 km/hr


Hope this will be helping you....

Answer 2

Distance travelled = 50*3/4=37. 5km
(1) time taken = 37. 5/30= 1Hr 15min
(2)
$average \: speed = \frac{total \: distance \: travelled}{total \: time \: taken}$
=(37. 5*2)/(2 hr)=37. 5kmph