Lesson One unusual Travel problem

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One unusual Travel problem

Jonny on his bicycle and Kevin on his motorcycle started to move simultaneously at 8:00 am from the points A and B on a road toward each other.
Each is moving at his own constant speed.
Jonny and Kevin met at noon (12 o'clock at midday) and continued to move without stopping each on his way at the same speed.
Kevin arrived to the point A at 2:00 pm.
At what time Jonny arrived to the point B?

Solution

Note that the distance is not a given in this problem. Nevertheless, we can solve it by applying elementary logic.

Figure 1 shows the road Jonny and Kevin are moving on. For simplicity, the road is shown as a straight line in the Figure 1.
Actually, it doesn't matter, and the road might be curved :-) The point C in the Figure 1 represents the meeting point.

According to the condition, Kevin spent 4 hours (from 8:00 am till noon) moving uniformly from his starting point B
to get the meeting point C. After that Kevin spent another 2 hours to get the point A.

Figure 1. The road between A and B

Since Kevin moved at a constant speed, it means that the distance from the point B to the point C is twice the distance from the point C to the point A.
This, in tourn, means that the Jonny's speed is two times lesser than that of Kevin because Jonny spent the same 4 hours to cover twice lesser distance from A to C.

Hence, Jonny will spend 2 x 4 hours = 8 hours to cover the distance from C to B moving in two times slower than Kevin. Therefore, Jonny will arrive to the point B
at 8:00 pm.

Answer. Jonny will arrive to the point B at 8:00 pm.

My other lessons on Travel and Distance problems in this site are

- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
- Using fractions to solve Travel problems

- Wind and Current problems
- More problems on upstream and downstream round trips
- Wind and Current problems solvable by quadratic equations
- Unpowered raft floating downstream along a river
- Selected problems from the archive on the boat floating Upstream and Downstream
- Selected problems from the archive on a plane flying with and against the wind

- Selected Travel and Distance problems from the archive

- Had a car move faster it would arrive sooner
- How far do you live from school?

- Another unusual Travel problem (Arnold's problem on two walking old women)

- Travel problem on a messenger moving back and forth along the marching army's column
- A person walking along the street and buses traveling in the same and opposite directions

    - Calculating an average speed: a train going from A to B and back
    - One more problem on calculating an average speed

    - Clock problems
    - Advanced clock problems
    - Problems on bodies moving on a circle

    - A train passing a telegraph post and passing a bridge
    - A train passing a platform
    - A train passing through a tunnel
    - A light-rail train passing a walking person
    - A train passing another train

    - A man crossing a bridge and a train coming from behind
    - A rower going on a river who missed the bottle of whiskey under a bridge
    - Non-traditional Travel and Distance problems

    - The distance covered by a free falling body during last second of the fall
    - The Doppler Shift
    - Entertainment Travel and Distance problems
    - OVERVIEW of lessons on Travel and Distance

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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