MATH SOLVE

4 months ago

Q:
# a. Set up an equation to represent the distance the cheetah covered in terms of t minutes running at maximum speed. Remember, units of distance and time must agree. Use the conversion information from the warm-up to write a rate in miles per minute.

Accepted Solution

A:

The distance travelled by an object at time t is given by: d = stwhere d is the distance, s is the speed and t is the time.

Given that the cheetah travels a maximum of 70mph, the distance travelled by the cheetah travelling at 70mph at time t is given by d = 70t

There are 60 mins in one hour, so the distance given in miles per minutes is d = 70/60t = 1.167 miles per minutes.

Part B:

Given that t = 10 minutes, the distance covered by the cheetah in 10 minutes is d = 1.167 x 10 = 11.67 miles.

Part C:

If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the first 8 minutes is given by

d = 1.167 x 8 = 9.33 miles.

Part D:

If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the second 8 minutes is given by

d = 40/60 x 8 = 5.33 miles

Part E:

The distance the cheetah traveled in the first 8 minutes more than in the second 8 minutes is given by

9.33 miles - 5.33 miles = 4 miles.

Part F:

The ratio of the distance travelled in the first 8 minutes to the distance travelled in the next minutes is given by

9.33 : 5.33 = 1.75 : 1.

Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.

Given that the cheetah travels a maximum of 70mph, the distance travelled by the cheetah travelling at 70mph at time t is given by d = 70t

There are 60 mins in one hour, so the distance given in miles per minutes is d = 70/60t = 1.167 miles per minutes.

Part B:

Given that t = 10 minutes, the distance covered by the cheetah in 10 minutes is d = 1.167 x 10 = 11.67 miles.

Part C:

If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the first 8 minutes is given by

d = 1.167 x 8 = 9.33 miles.

Part D:

If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the second 8 minutes is given by

d = 40/60 x 8 = 5.33 miles

Part E:

The distance the cheetah traveled in the first 8 minutes more than in the second 8 minutes is given by

9.33 miles - 5.33 miles = 4 miles.

Part F:

The ratio of the distance travelled in the first 8 minutes to the distance travelled in the next minutes is given by

9.33 : 5.33 = 1.75 : 1.

Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.