Photo:
THE MIRROR
Steffi and Sarah meet for running training at a quarry lake around which a running track leads.
Both stand next to each other and start in opposite directions.
It's a minute before they meet again.
In the second training session, they change the procedure: they stand next to each other again, but start in the same direction.
It's an hour before they meet again.
Obviously, Steffi and Sarah run at different speeds.
What is their speed ratio?
Note: We assume that both runners run at the same speed in both training sessions.
The ratio of speeds is
61/59
.
The solution is simpler than you might initially think.
a
and
b
are speeds of the two women.
We use rounds per minute as the unit of measurement, which simplifies further calculations.
In the first training session, both run one minute each and do one lap together.
So valid
a*1 min + b* min = 1 round
To be able to calculate better, simply leave out the units of measurement:
a + b = 1
In the second training session, both run 60 minutes each and one woman does one more lap.
Then:
60a = 60b + 1
Now we rearrange the upper equation for b (b = 1 - a) and plug it into the lower equation:
60a = 60(1-a) + 1
120a = 61
a = 61/120
With a + b = 1 we get
b = 59/120
and for the ratio of speeds
61/59
.
I discovered this puzzle on the Mathigon platform.
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