Distance, rate and time problems: head starts, meeting and wind or current

Answer Key - Grade 9 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Bo and a friend are 12 miles apart on a bike trail and ride toward each other at 10 mph and 14 mph. How many hours until they meet?

   0.5 hours
2. 2.

   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?

   1.5 hours
3. 3.

   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
4. 4.

   In Luz's meeting problem, why is t the same for both travelers?

   • They go the same speed
   • They travel until the same moment
   • They cover the same miles
5. 5.

   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?

   • 1t
   • t + 1
   • t − 1
6. 6.

   In Milo's head-start problem, the follower catches up. What is equal at that moment?

   • The two distances
   • The two travel times
   • The two speeds
7. 7.

   Noah bikes at 12 mph with a 1-hour head start; a car follows at 20 mph for t hours. Which equation fits?

   • 12t = 20(t + 1)
   • 12(t + 1) = 20t
   • 12t + 20t = 1
8. 8.

   A plane flies 450 mph in still air with a 30 mph tailwind on Pia's trip. What is its ground speed?

   • 480 mph
   • 450 mph
   • 420 mph
9. 9.

   Ren's canoe goes 8 mph in still water. The river flows at 2 mph. How fast does it go upstream?

   • 6 mph
   • 10 mph
   • 16 mph
10. 10.

    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