Willy left the hardware store and traveled toward the recycling plant at an average speed of 33 km/h. Mary left two hours later and traveled in the same direction but with an average speed of 55 km/h. How long did Willy travel before Mary caught up?

Willy's average speed of 33 km/h and Mary's average speed of 55km/h. Mary start traveling 2 hours after willy started her journey. After 2 hours Willy traveled 33 x 2 km = 66km. To find when they meet, we need to find the LCM of 33 and 55.

LCM (33 and 55) = 165.

willy reached from the hardware shop165km after 5hours (165/33) and Mary reached 165km from the shop 3 Hours (165/55)

willy traveled 2 hours earlier than Mary. So Willy and Mary reaches 165km in same time. Willy take more time to reach there. so the answer is 165km in 5hours traveled by Willy before Mary caught up.

Distance traveled by Willy before Mary caught up = 165 km.

Explanation;

Distance traveled before caught up is same for both Mary and Willy.

Let time taken by Mary be t hours, time taken by Willy = (t+2) hours.

We have distance traveled = Speed x Time taken

Distance traveled by Willy = 33 x (t + 2) = 33t + 66

Distance traveled by Mary = 55t

Equating both

33t + 66 = 55t

22 t = 66

t = 3 hours.

Distance traveled by Willy = 33t + 66 = 33 x 3 + 66 = 165 km.