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arlik [135]
3 years ago
14

Buses to exeter leave a bus station every 20 minutes.Buses to Plymouth leave the bus station every 16 minutes A bus to exeter an

d a bus to plymouth both leave the bus station at 8am.When will buses to exeter and plymouth next leave the bus station at the same time
Mathematics
1 answer:
Eva8 [605]3 years ago
6 0
9:20 am
Lcm is 80 so 80 minutes after 8 am is 9:20
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Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How
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Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood  = K hrs

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As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood  = (K- 3) hrs

So, the per hour rate of Joe  = (\frac{1}{K-3})

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them  = (\frac{1}{2})

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\implies (\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})

Now, solving for the value of K , we get:

(\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})\\\implies  \frac{(K-3) + K}{K (K-3)}  = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K  + 6=  0\\\implies K^2 - 6K - K  + 6=  0\\\implies K(K-6) -1(K - 6)=  0\\\implies (K-6)(K-1) = 0

Implies either K = 6 Or K = 1

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⇒ K  = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0
3 years ago
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