Distance, rate and time problems: head starts, meeting and wind or current
Grade 9 Math Worksheet
Circle the best answer, or write your answer on the line.
Ari's cousins live 150 miles away. Both families drive toward each other, at 40 mph and 35 mph, to meet for a picnic. How many hours until they meet?
Two trains start 270 miles apart and head toward each other at 80 mph and 100 mph. Esme wonders: how many hours until they pass?
Families drive toward each other from 150 miles apart at 40 and 35 mph. Which equation does Jun use?
- 40t + 35t = 150
- 40t − 35t = 150
- 40 + 35 = 150t
Kira and a friend ride toward each other from 12 miles apart at 10 and 14 mph. Which equation fits?
- 24 + t = 12
- 10t + 14t = 12
- 10t = 14t + 12
In Luz's meeting problem, why is t the same for both travelers?
- They travel until the same moment
- They cover the same miles
- They go the same speed
Esme bikes at 12 mph, and a parent follows 1 hour later at 20 mph. What is Esme's time if the parent drives t hours?
- t − 1
- t + 1
- 1t
In Milo's head-start problem, the follower catches up. What is equal at that moment?
- The two travel times
- The two speeds
- The two distances
Noah bikes at 12 mph with a 1-hour head start; a car follows at 20 mph for t hours. Which equation fits?
- 12t + 20t = 1
- 12(t + 1) = 20t
- 12t = 20(t + 1)
A plane flies 450 mph in still air with a 30 mph tailwind on Pia's trip. What is its ground speed?
- 450 mph
- 480 mph
- 420 mph
A plane flies p mph in still air into a headwind of w mph. Which expression gives its ground speed for Tala's flight?
- p − w
- p × w
- p + w