Grade 9 · Math · Algebra 1

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

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

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

Grade 9 Math Worksheet

NameDate

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

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?
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?
3.
Families drive toward each other from 150 miles apart at 40 and 35 mph. Which equation does Jun use?
- 40t + 35t = 150
- 40 + 35 = 150t
- 40t − 35t = 150
4.
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
5.
In Luz's meeting problem, why is t the same for both travelers?
- They cover the same miles
- They travel until the same moment
- They go the same speed
6.
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
- 1t
- t − 1
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)
- 12t + 20t = 1
- 12(t + 1) = 20t
8.
A plane flies 450 mph in still air with a 30 mph tailwind on Pia's trip. What is its ground speed?
- 450 mph
- 420 mph
- 480 mph
9.
Ren's canoe goes 8 mph in still water. The river flows at 2 mph. How fast does it go upstream?
- 16 mph
- 10 mph
- 6 mph
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

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.

More algebra 1

See all Algebra 1

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records