A boy stated from his house on bicycle at 10 am at a speed of 12 km per hour. His elder brother started after 1 hr 15 min on scooter along the same path and caught him at 1.30 pm. The speed of the scooter will be (in km/hr) ?

Solution(By Examveda Team)

Total distance covered by man in (1.30 pm - 10.00 am)
= $$3\frac{1}{2}$$ hours at a speed of 12 km/hr
= 12 × $$3\frac{1}{2}$$
= 42 km (Total distance)
Time taken by his elder brother to catch him :
= $$3\frac{1}{2}$$ - 1 hour 15 min
∴ Brother's time
= 3 hr 30 min - 1 hr 15 min
= 2 hr 15 min
= $$2\frac{15}{60}$$
= $$2\frac{1}{4}$$
= $$\frac{9}{4}$$ hours
⇒ Brother's speed :
= $$\frac{{42}}{{\frac{9}{4}}}\,\,\left( {{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Time}}}}} \right)$$
= $$18\frac{2}{3}{\text{ km/hr}}$$