We read your photo as:

Two towns are 60 km apart. James leaves Town A at 8.00 a.m. travelling at 20 km/h. Peter leaves Town B at 9.00 a.m. travelling at 30 km/h towards James. How long after 8.00 a.m. do they meet?

Mathematics

ScanSolve AI Answer

Answers

2 parts
a

1 hour 48 minutes\text{1 hour 48 minutes}

b

9:48 a.m.\text{9:48 a.m.}

Step-by-step solution

7 steps

Here are the solutions to the problems:

13. Two towns are 60 km apart. James leaves Town A at 8.00 a.m. travelling at 20 km/h. Peter leaves Town B at 9.00 a.m. travelling at 30 km/h towards James.

Part a· 6 steps

How long after 8.00 a.m. do they meet?

  1. Calculate the distance James travels from 8:00 a.m.

    to 9:00 a.m.

    Distance covered by James=Speed×Time=20 km/h×1 h=20 km\text{Distance covered by James} = \text{Speed} \times \text{Time} = 20 \text{ km/h} \times 1 \text{ h} = 20 \text{ km}

  2. Calculate the remaining distance between the towns at 9:00 a.m.

    Remaining distance=Total distance−Distance covered by James=60 km−20 km=40 km\text{Remaining distance} = \text{Total distance} - \text{Distance covered by James} = 60 \text{ km} - 20 \text{ km} = 40 \text{ km}

  3. Calculate their relative speed since they are moving towards each other.

    Relative speed=James’s speed+Peter’s speed=20 km/h+30 km/h=50 km/h\text{Relative speed} = \text{James's speed} + \text{Peter's speed} = 20 \text{ km/h} + 30 \text{ km/h} = 50 \text{ km/h}

  4. Calculate the time it takes for them to meet after 9:00 a.m.

    Time to meet=Remaining distanceRelative speed=40 km50 km/h=0.8 hours\text{Time to meet} = \frac{\text{Remaining distance}}{\text{Relative speed}} = \frac{40 \text{ km}}{50 \text{ km/h}} = 0.8 \text{ hours}

  5. Convert the time to minutes.

    0.8 hours×60 minutes/hour=48 minutes0.8 \text{ hours} \times 60 \text{ minutes/hour} = 48 \text{ minutes}

  6. Calculate the total time after 8:00 a.m.

    until they meet.

    Total time=1 hour (from 8:00 to 9:00)+48 minutes=1 hour 48 minutes\text{Total time} = 1 \text{ hour (from 8:00 to 9:00)} + 48 \text{ minutes} = 1 \text{ hour } 48 \text{ minutes}

    They meet 1 hour 48 minutes after 8:00 a.m.

    1 hour 48 minutes\boxed{\text{1 hour 48 minutes}}

Part b

9:48 a.m.\text{9:48 a.m.}

At what time do they meet?

  1. Determine the meeting time.

    They start moving towards each other at 9:00 a.m. and meet 48 minutes later.

    Meeting time=9:00 a.m.+48 minutes=9:48 a.m.\text{Meeting time} = 9:00 \text{ a.m.} + 48 \text{ minutes} = 9:48 \text{ a.m.} 9:48 a.m.\boxed{\text{9:48 a.m.}}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA car moving at an average speed of 40km/h left town A at 7:00 a.m for town B which is 40km away…QTwo towns A and B are 400 km apart. A motor cyclist travelling at an average speed of 60km/h left…QA bus travels at 90 km/h. A car leaves 2 hours and 20 minutes after the bus, traveling at 110 km/h…QThe distance between two towns A and B is 760 km. A bus left A at 0815 hours and traveled towards B…QTwo vehicles start at 8:30 a.m. and travel towards each other over a distance of 240 km. If their…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp