Question

A turtle and bunny have a race. Running a straight line of 42km.

1. What is the average speed of the turtle knowing that it will take him 6 hours to run it?

2. The bunny will obviously be faster, being able to run 10 km/hr. How long will it take him to run it?

3. If the bunny gives the turtle a 1 hr head start, how far will the turtle get?

4. If the bunny gives the turtle a 1 hr head start, how long will it take him to catch up?

5. If the bunny decides to take a 3 hr nap during the race instead of giving the turtle a headstart, who will win the race?

Answer 1

1.

D = distance traveled by turtle = 42 km = 42000 m

t = time taken = 6 h

average speed of turtle is given as

V_tur = D/t

V_tur = 42/6

V_tur = 7 km/h

2.

V_bunny = speed of bunny = 10 km/hr

D = distance traveled = 42 km

time taken by bunny is given as

t_bunny = D/V_bunny

t_bunny = 42/10

t_bunny = 4.2 hr

3.

V_tur = average speed of turtle = 7 km/h

t_head = time of headstart = 1 hr

d = distance between bunny and turtle

Distance between bunny and turtle after time of headstart is given as

d = V_tur t_head

d = (7) (1)

d = 7 km

4.

t_catch = time for the bunny to catchup

Time for catchup is given as

t_catch = d/(V_bunny - V_tur)

t_catch = 7/(10 - 7)

t_catch = 2.33 h

5.

t_turtle = time taken by turtle to complete the race = 7 h

t_nap = time spent in taking nap by bunny = 3 h

t = remaining time for bunny to travel the distance = 4.2 h

t_bunny = time taken by bunny to complete the race = 3 + 4.2 = 7.2 h

Since

t_turtle < t_bunny

hence turtle wins the race