Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x = distance and t = time. Additionally, [speed x time = distance]. Won't the van catch up when the distances are equal?

Question

Mathematics

Mohamed Rocha

25 September, 15:29

Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x = distance and t = time. Additionally, [speed x time = distance]. Won't the van catch up when the distances are equal?

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Journey Bradshaw · Answer 1

= 15mins 18 seconds. The storm chaser van drove 13.53 miles to catch up with the storm which obviously has moved less than 0.53 miles as it was same time but multiplied below by 0.5 per minute as speed per minute is 0.5 for the storm. See right at the end the storm only moved 1.11 mile.

Step-by-step explanation:

We count in 1 minutes

54 mph = 54/60 = 0.9 miles per minute

Storm = 13 m + 1 minute is;

33/60 = 0.55 miles = 11/20

M = (16 7/10 * 9/10x) = (3 7/10 * 11/20y) + 13

M = 15 3/10x = (407/200y + 13) (407/200 = y starting value + 13)

M = 15 3/10x = 15 3/10 = 16 7/10x (the same as 16 7/10 * 9/10 for x)

M = 15 3/10 x = 15 3/10 = 15.03

M = 16 7/10x / 9/10y (is also the same as 186/1000)

X = 185⁄1000 = 37⁄200xy x 16 7/10 (as starting value)

7/10 of 60 = 42 minutes

3/10 of 60 = 18 minutes

x = 15 mins 18 seconds.

y = 15 mins 18 seconds.

as 0.005 left over for y 3/10 was actually 15.035 gives us 0.005 of 60 can not be rounded up to a second.

However as we started with 16mins and 7/10 we can see that we multiplied by 9/10 so when we divide 16 7/10 by 9/10 we find 185⁄1000 = 37⁄200

To equal the mileage of the storm of where we multiplied 3 7/10 by 17/10

= 37/200 just the same

We added 13 miles of the storm to find each was multiplied by the larger x sum 9/10 and y was multiplied

As 35/200 + 13 =

13 37/200

37/200 of 60 = 11.1 = 11.06 minutes which is

= 15.04 % more for y as 13 + 2 mins + 06 seconds = 15.06 = 15.035

The percentage looks the same but valued different as 2 of 13 as a percentage is multiplied as 13 x 15.04% to equal the 2 of 15 miles as 15.04%.

To find how many miles we go back and see 15.035 = 15 7/200

Then we multiply this by 0.9 miles for the storm van

= 15 7/200 x 0.9 = 13.5315 = 13.53 miles

For the storm itself we can prove 0.53 increase of mileage

417/200 x 0.53 = 1.10505 = 1.11 miles. rounded up