Grade 9 · Math · Algebra 1

9th grade Distance, rate and time problems: head starts, meeting and wind or current worksheet

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

Grade 9 Math Worksheet - Challenge Me

NameDate

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

A bus leaves at 40 mph. 1 hour later, a car carrying Ari and a forgotten lunch follows at 60 mph. How many hours does the car drive to catch up?
Bo's friend starts biking at 12 mph. 1 hour later, Bo follows at 18 mph. How many hours does Bo ride to catch up?
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.
Jun's canoe goes 10 mph downstream and 6 mph upstream. How fast does it go in still water?
- 16 mph
- 8 mph
- 4 mph
5.
Kira's canoe goes 10 mph downstream and 6 mph upstream. How fast is the current?
- 4 mph
- 2 mph
- 8 mph
6.
Luz's boat goes 7 mph in still water on a river flowing 2 mph. How long is an 18-mile trip downstream?
- 2.57 hours
- 2 hours
- 3.6 hours
7.
Milo says a 30 mph headwind makes a 450 mph plane fly at 480 mph. Agree or disagree?
- Agree: any wind adds to the plane's speed
- Disagree: a headwind slows it to 420
- Agree: 450 + 30 is 480
8.
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
- Agree: the current adds 2 mph
- Disagree: upstream it goes 6 mph
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.
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

9th grade Distance, rate and time problems: head starts, meeting and wind or current worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Distance, rate and time problems: head starts, meeting and wind or current. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can use distance = rate × time, and its rearrangements, with one row per traveler.
I can find when two travelers meet (rates add) or when one catches up (rates subtract).
I can write the one-letter equation for a head start or a meeting.
I can add or subtract a wind or current, and check an answer against the story.

Standard: A-CED.A.1, N-Q.A.1

Words to know

rate: How far something goes in each hour, like 45 mph

head start: Extra time or distance one traveler has before the other starts

tailwind: Wind pushing from behind, adding speed

headwind: Wind blowing against, taking speed away

current: Moving water that speeds a boat up or slows it down

Common mistakes

Your child added the rate and the time. Distance is rate times time.

Your child used only one traveler's speed. When two travelers move toward each other, the gap closes at both speeds added.

Your child added the two speeds. When one traveler chases another, the gap closes at the difference of the speeds.

What to say

Ask: how far in one hour, then in all the hours?

Questions parents ask

What is the most common mistake with distance, rate and time problems: head starts, meeting and wind or current?

Your child added the rate and the time. Distance is rate times time.

How can I help my child with distance, rate and time problems: head starts, meeting and wind or current?

Ask: how far in one hour, then in all the hours?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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