Vic can beat Harold by one tenth of a mile in a two mile race. Harold can beat Charlie by one fifth of a mile in a two mile race. If Vic races Charlie, how far ahead will Vic finish?
A)
0.15 miles
(B)
0.22 miles
(C)
0.25 miles
(D)
0.29 miles
(E)
0.33 miles
I find 0.31 miles tell me what is wrong please:
v/h=(2 1/10)/2 = 1.05
h/c=(2 1/5)/2=1.1
v/h * h/c= v/c
1.05*1.1=1.155
v/2=1.155
v=2.31
so 0.31 miles more then charlie?
Your mistake is right at the start:
v/h=(2 1/10)/2 = 1.05
Harold did not run 2 miles, since Victor stopped the race when he won. You should have said
v/h= 2/(1 9/10)
which makes a small difference. Same for Harold and Charlie.
Your calculation steps and understanding are correct. However, there seems to be a mistake in calculation at the end.
When you calculated v/h * h/c, you obtained the value of 1.155. However, this value represents the ratio of Vic's speed to Charlie's speed in the race. It does not directly represent the distance by which Vic will finish ahead of Charlie.
To find the distance by which Vic will finish ahead of Charlie, you need to multiply the distance of the race (2 miles) by the ratio v/c.
Therefore, the correct calculation would be:
v/2 = 1.155
v = 1.155 * 2 = 2.31 miles
So, Vic will finish 2.31 - 2 = 0.31 miles ahead of Charlie.
Your calculations are close, but there seems to be a slight error in your final calculation. Let's go through the steps again to find the correct answer.
1. Let's start by comparing Vic and Harold's racing speeds. It is given that Vic can beat Harold by one-tenth of a mile in a two-mile race. So, the ratio of their speeds is v/h = 1.1/2 = 0.55.
2. Next, let's compare Harold and Charlie's racing speeds. It is given that Harold can beat Charlie by one-fifth of a mile in a two-mile race. So, the ratio of their speeds is h/c = 0.2/2 = 0.1.
3. Now, let's find the ratio of Vic's speed to Charlie's speed. We can multiply the ratios from steps 1 and 2: v/c = (v/h) * (h/c) = 0.55 * 0.1 = 0.055.
4. To find how far ahead Vic will finish compared to Charlie, we can multiply the ratio we found in step 3 by the distance of the race, which is 2 miles: (v/c) * 2 = 0.055 * 2 = 0.11 miles.
Therefore, the correct answer is (A) 0.11 miles. Vic will finish 0.11 miles ahead of Charlie in the race.