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Engineers are digging a 3200-foot-long tunnel at a constant rate. After 5 months, the engineers still need to dig 1700 feet to finish the project. How much time does it take to complete the tunnel from start to finish?

Will the engineers have enough time if the project was started in December 2020 and the deadline to finish the project was in August 2021? Please explain your answer for yes or no.

Hint:
y=mx+b (slope-intercept form)
x=time
y=distance
b=3200
Start & Finish: ??
Total length=3200ft
Left over=1700ft after 5 months of digging

help/

Respuesta :

thenightarcher

Answer:

Part A answer: 10 2/3 months

Part B answer: No

Step-by-step explanation:

Using what we gathered from the word problem, and the hint, we know that y = distance, x = time, and b = 3200.

3200 is the total number of ft meant for the hole to be dug. If we've been digging for 5 months, and we have 1700 ft yet to be dug, then after 5 months we have dug (3200 - 1700 =) 1500 ft in 5 months.

-1500 ft/5 months = 300 ft/month

-Digging the final 1700 ft will take 5 2/3 months

^ Using this information, we know that the total number of months it takes to dig the entirety of the tunnel is 10 2/3

In the second part of the problem, we're asked to determine whether or not a deadline of August 2021 was enough time to complete the 10 2/3 month-long project if the digging began in December of 2020.

If said project commenced in December 2020, and the deadline was August 2021, then there would be 1, 2, 3, 4, 5, 6, 7, 8... Roughly 8 1/2 months to complete the tunnel. 10 2/3 months is > (greater than) 8 1/2 months. So, no. That start-to-finish deadline would not be enough time.

Good luck!!

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