Question

PLZ HELP!!!! The distance between the cities Atlanta and Indianapolis is 540 miles. A motorcycle's speed is 48 mph. For a car it takes 2.25 hours less to cover same distance than for the motorcycle. How long does it take them to meet, if they start moving towards each other simultaneously?

Answer 1

Answer: 5 hours

Step-by-step explanation:

Given: The distance between the cities Atlanta and Indianapolis=540 miles

The speed of motorcycle= 48 mph

Since, $Time=\frac{Distance}{speed}$

$\\\Rightarrow\text{Time taken by motorcycle to travel}=\frac{540}{48}=11.25\ hours$

Thus, time taken by car to travel the distance= 11.25-2.25= 9 hours

$\\\Rightarrow\text{Speed of car}=\frac{540}{9}=60\ mph$

Let t be the time at which they will meet if they are moving towards each other  simultaneously.

Then Distance covered by Motorcycle+Distance covers by car= 540 miles

$\\\Rightarrow48t+60t=540\\\Rightarrow108t=540\\\Rightarrow\ t=5$

Thus they will meet in 5 hours, after which time the motorcycle will have traveled $48\times5=240\miles$

and the car will have traveled $60\times5=300\miles$