A motorist left town X at 08 00 for town Y situated 120km away, travelling at a constant speed of v km/hr, so as to arrive at Y
at 10 40. But, after travelling for 80 minutes, his car developed engine trouble and he had to stop for 30 minutes to repair it. Then he continued his journey at a speed of u km/hr, so as to arrive at Y at 10 40. a) sketch the distance-time graph for the car. b) Calculate the valued of v and u.
2 answers:
To answer a, it is important that we have the values of v and u first. From 8:00 to 10:40, there are approximately 160 minutes or 2.67 hours.
(1) Travelling v km/h for 80 minutes (4/3 hours)
D = (4/3 v)
(2) Stopped for 30 minutes.
D₂ = (0)(0.5) = 0
(3) Traveled with speed of u for the rest of the trip.
D₃ = (2.67 - 0.5 - 4/3)(u) = 5u/6
Adding up the distances covered,
D = 120 = 4v/3 + 5u/6
Also, as per given,
((8/3)(v)) = 120
v = 45 km/h
From the equation above,
4(45)/3 + (5)(u)/6 = 120
The value of u from the equation is 72 km/h.
(b) v = 45 km/h and u = 72 km/h.
(a) The graph is attached.
(1) Travelling v km/h for 80 minutes (4/3 hours)
D = (4/3 v)
(2) Stopped for 30 minutes.
D₂ = (0)(0.5) = 0
(3) Traveled with speed of u for the rest of the trip.
D₃ = (2.67 - 0.5 - 4/3)(u) = 5u/6
Adding up the distances covered,
D = 120 = 4v/3 + 5u/6
Also, as per given,
((8/3)(v)) = 120
v = 45 km/h
From the equation above,
4(45)/3 + (5)(u)/6 = 120
The value of u from the equation is 72 km/h.
(b) v = 45 km/h and u = 72 km/h.
(a) The graph is attached.
You might be interested in
Answer:
a) p=0.021
b) p=0.029
c) Exactly one audit: P=0.0965
More than one audit: P=0.0042
Step-by-step explanation:
a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:
If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:
b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:
There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.
To calculate the probability that more than one will be audited, we use the same distribution:
There is a probability of 0.0042 that more than one out of a sample of five taxpayers with incomes under $100,000 will be audited.
Please note that in proving this, I have used trigonometric identities other than just the sine angle-addition formula.
