Tim and Rick both can run at speed Vr and walk at speed , Vw with Vr > vw. They set off together on a journey of distance . Rick walks half of the distance and runs the other half. Tim walks half of the time and runs the other half.
How long does it take Tim to cover the distance?
Express the time taken in terms of Vr, Vw, and D.
To find the time taken by Tim to cover the distance, we need to consider the time taken for walking and the time taken for running.
Let's start by calculating the time taken for walking. Since Rick walks half the distance, we know that Rick takes D/2Vw time to complete this portion.
Now let's calculate the time taken for running. Tim walks half the time and covers half the distance. So, Tim runs for D/2 and his running speed is Vr. Thus, the time taken for running is (D/2)/Vr = D/2Vr.
To find the total time taken by Tim, we add the time taken for walking and the time taken for running:
Total time taken by Tim = Time taken for walking + Time taken for running
= D/2Vw + D/2Vr
So, the time taken by Tim to cover the distance is (D/2Vw + D/2Vr), which can be written as D(Vr + Vw)/2VwVr.
Therefore, the time taken by Tim to cover the distance is D(Vr + Vw)/2VwVr.