A tortoise and a hare both ran at a
constant speed along the same 1000-meter route. The tortoise took 90 minutes to
finish. The hare started 40 minutes after
the tortoise. The hare overtook the tortoise when
they both had 200 meters left. Work out the hare’s speed.
This question is about speed,
distance, and time. So we need to recall the formula
triangle, which tells us how these three quantities are related. Let’s look at the information in
the question carefully. We’re told that the tortoise took
90 minutes to finish the 1000-meter route.
As the tortoise runs a constant
speed, we can scale this down and see that the tortoise runs 100 meters in nine
minutes. The hare overtakes the tortoise
when they have 200 meters left. And based on the rate at which the
tortoise is running, this 200 meters would take the tortoise 18 minutes.
Now, let’s think about what the
hare is doing while the tortoise is on their 90-minute journey. The question tells us that the hare
starts 40 minutes after the tortoise. The hare overtakes the tortoise
when they both have 200 meters left. Remember the tortoise can move 200
meters in 18 minutes. So this is 72 minutes into the
90-minute journey. To calculate the hare’s speed, we
need to know how long it took the hare to travel a particular distance. So we’ll use the portion of the
journey between when the hare starts and when he overtakes the tortoise.
As the hare has 200 of the 1000
meters left, then the distance that he’s travelled is 800 meters. The time taken is the difference
between 72 and 40. So it’s 32 minutes. We know then that the hare has
travelled 800 meters in 32 minutes. Using the formula triangle, we know
that the calculation for speed is distance divided by time. So this is 800 divided by 32.
To perform this calculation, we can
keep dividing both the numerator and denominator of the fraction by two. 800 over 32 becomes 400 over 16 and
then 200 over eight and then 100 over four. 100 over four is equal to 25.
So the hare’s speed is 25 meters