The Chunnel connects the United Kingdom and France by a railway tunnel under the English Channel. The British started tunneling 2.5 months before the French and averaged 0.63 Kilometer per month. The French averaged 0.47 kilometer per month. When the two sides met, they had tunneled 37.9 Kilometers. How many kilometers of tunnel did each country build? If the French started tunneling on February 28, 1988, approximately when did the two sides meet?
I want to know how you solve the problem..I forgot how to set it up.
Thank You!
let the distance covered by the British be x km
then the distance covered by the French is 37.9-x km
Let the time taken by the French be t months
then the British dug for t+2.3 months
You can form two equations using "Distance = Rate x Time"
1) Distance dug by British: x = (0.63)(t+2/5)
2) Distance dug by French: 37.9-x = 0.47t
from 2) x = 37.9 - 0.47t
now equate them, both are equal to x, and solve for t.
Put that back into either 1) or 2) to get x
good luck, let me know what you got
Let T be the number of months that the English dug the chunnel. The French then dug for T-2.5 months.
The length dug when they met was
0.63 T + 0.47(T-2.5) = 37.9
Now you can solve for T and compute the amount dug by each. Add
(T months) x 30.4(average days/month)
to February 28,1988 to get the date they met.
I seem to be having a rough time getting used to my new keyboard on my new Mac
<then the British dug for t+2.3 months>
should say
then the British dug for t+2.5 months
and <1) Distance dug by British: x = (0.63)(t+2/5) >
should say
1) Distance dug by British: x = (0.63)(t+2.5)
To solve this problem, let's set up some equations and variables.
Let's assume that the British started tunneling on January 1, 1988. Since they started tunneling 2.5 months before the French, they would have been tunneling for 2.5 months before February 28, 1988.
So, the British started tunneling on November 15, 1987.
Let's also assume that "x" represents the number of months it took for both sides to meet.
Now, let's calculate the distance each country built:
The British averaged 0.63 km/month and had a head start of 2.5 months, so the distance they built is:
Distance built by the British = 0.63 km/month * (x + 2.5 months)
The French averaged 0.47 km/month and started tunneling on February 28, 1988, so the distance they built is:
Distance built by the French = 0.47 km/month * x months
According to the problem, when the two sides met, they had tunneled 37.9 kilometers. Therefore, we can set up the equation:
Distance built by the British + Distance built by the French = Total Distance
0.63 km/month * (x + 2.5 months) + 0.47 km/month * x months = 37.9 km
Now we can solve this equation to find the value of "x".
0.63x + 0.63 * 2.5 + 0.47x = 37.9
0.63x + 1.575 + 0.47x = 37.9
1.1x + 1.575 = 37.9
1.1x = 36.325
x ≈ 33.02
Therefore, it took approximately 33.02 months for both sides to meet.
Now we can substitute this value back into the equations to find the distance each country built:
Distance built by the British = 0.63 km/month * (33.02 months + 2.5 months) ≈ 23.23 km
Distance built by the French = 0.47 km/month * 33.02 months ≈ 15.51 km
So, the British built approximately 23.23 kilometers of tunnel, while the French built approximately 15.51 kilometers of tunnel.
Therefore, the two sides met after approximately 33.02 months, which is around late February or early March in 1991.