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

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   A truck leaves at 50 mph. 2 hours later, Esme's train leaves the same town on a parallel route at 75 mph. How many hours until the train catches up?

   4 hours
2. 2.

   Jun's canoe goes 10 mph downstream and 6 mph upstream. How fast does it go in still water?

   • 4 mph
   • 16 mph
   • 8 mph
3. 3.

   Kira's canoe goes 10 mph downstream and 6 mph upstream. How fast is the current?

   • 8 mph
   • 4 mph
   • 2 mph
4. 4.

   Luz's boat goes 7 mph in still water on a river flowing 2 mph. How long is an 18-mile trip downstream?

   • 3.6 hours
   • 2 hours
   • 2.57 hours
5. 5.

   Milo says a 30 mph headwind makes a 450 mph plane fly at 480 mph. Agree or disagree?

   • Disagree: a headwind slows it to 420
   • Agree: any wind adds to the plane's speed
   • Agree: 450 + 30 is 480
6. 6.

   Noah says a canoe going 8 mph in still water moves 10 mph upstream in a 2 mph current. Agree or disagree?

   • Agree: rivers speed canoes up
   • Disagree: upstream it goes 6 mph
   • Agree: the current adds 2 mph
7. 7.

   Pia says a 60 mph car closes a gap on a 40 mph bus at 100 mph. Agree or disagree?

   • Disagree: it gains 20 mph
   • Agree: add the two speeds together
   • Agree: both are moving
8. 8.

   Ren finds that families 150 miles apart, at 40 and 35 mph, meet after 2 hours. Which check shows it works?

   • 150 ÷ 2 = 75 mph each
   • 40 + 35 = 75 miles
   • 80 + 70 = 150 miles
9. 9.

   A 40 mph bus leaves 1 hour before a 60 mph car. Tala says the car catches up after 2 hours. Which check fits?

   • Both have gone 100 miles
   • Both have gone 120 miles
   • The car has gone 60 miles
10. 10.

    Zee gets 120 miles for a 4-hour walk at 3 mph. Why is that answer unreasonable?

    • Walkers go 30 mph
    • Walking 4 hours covers about 12 miles
    • Time should be multiplied by 30