Question

At $ 9{\rm{ am}} $ a car $ \left( A \right) $ began a journey from a point, travelling at $ 40{\rm{ mph}} $ . At $ 10{\rm{ am}} $ another car $ \left( B \right) $ started travelling from the same point at $ 60{\rm{ mph}} $ in the same direction as car $ \left( A \right) $ . At what time will car $ B $ pass car $ A $ ?

Answer 1

Hint: The speed at which car $ A $ is travelling is $ 40{\rm{ mph}} $ and the distance for car $ A $ is given as $ 40t $ and to find the distance travelled by the car $ B $ we will multiply $ 60 $ with $ t - 1 $ . We know the direction of the car $ A $ is equal to car $ B $ .

Complete step-by-step answer:
Given that At $ 9{\rm{ am}} $ a car $ \left( A \right) $ began a journey from a point, travelling at $ 40{\rm{ mph}} $ .
At $ 10{\rm{ am}} $ another car $ \left( B \right) $ started travelling from the same point at $ 60{\rm{ mph}} $ in the same direction as the car \[\].
From the given information we know that the direction $ {D_1} $ travelled by car $ A $ will be,
 $ {D_1} = 40t $
Given that a car \[\]starts at the time $ 10{\rm{ am}} $ and will therefore have spent one hour less then car $ A $ when it passes it, here the distance $ {D_2} $ travelled by car $ B $ is given by,
 $ {D_2} $ is equal to $ 60\left( {t - 1} \right) $ .
When car $ B $ passes car $ A $ , they are at the same distance from the starting point and therefore $ {D_1} $ is equal to $ {D_2} $ .
Hence, by substituting the values of $ {D_1} $ and $ {D_2} $ we get the equation as,
 $ 40t = 60\left( {t - 1} \right) $
Using the distributive property, distributive property says that $ a\left( {b + c} \right) = ab + ac $ .
Hence,
 $ \begin{array}{l}
40t = 60t - 60\\
40t - 60t = - 60\\
 - 20t = - 60
\end{array} $
Divide both sides by $ 20 $ we get
\[\].
As the time passes when the car $ A $ starts the journey is $ 9{\rm{ am}} $ .
We add the time as $ 3 $ hours to it and get the time as $ 12{\rm{ am}} $ .
Hence the time at which the car $ B $ passes the car $ A $ is at $ 12{\rm{ am}} $ .

Note: Every time the car $ A $ and car $ B $ will not have the same formula. Please be careful with the equations. We have taken the car $ A $ direction is equal to the direction of car $ B $ since they have given. If it is not given in the question, then don’t take that they are equal.