In addition to spanning a river which is 50 metres wide, a straight bridge also has considerable overlap of both banks of the river. One third of the bridge overlaps one bank and one half overlaps the other bank. The total length,in metres, of this bridge is
A. 100
B.150
C.200
D.300
E.400
1/2 + 1/3 = 5/6
so, only 1/6 of the bridge is over water.
x/6 = 50
...
Let's denote the total length of the bridge as L.
One-third of the bridge overlaps one bank of the river, which means that (1/3)L is the length of the bridge overlapping that bank.
One-half of the bridge overlaps the other bank of the river, which means that (1/2)L is the length of the bridge overlapping that bank.
Since the bridge spans across the river, the sum of the lengths overlapping both banks will be equal to the width of the river.
So, we have the equation:
(1/3)L + (1/2)L = 50
Multiplying through by the least common denominator, which is 6, we get:
2L + 3L = 300
Combining like terms, we have:
5L = 300
Dividing both sides of the equation by 5, we get:
L = 60
Thus, the total length of the bridge is 60 meters.
Therefore, the correct answer is A. 100.
To find the total length of the bridge, we need to find the length of each of the overlapping sections and add them together.
Let's start by finding the length of the section that overlaps one bank. We know that one-third of the bridge overlaps one bank, and the entire bridge is 50 meters wide.
One-third of the bridge overlaps one bank:
Length of overlap on one bank = (1/3) * 50 meters = 50/3 meters
Next, let's find the length of the section that overlaps the other bank. We know that one-half of the bridge overlaps the other bank, and the entire bridge is 50 meters wide.
One-half of the bridge overlaps the other bank:
Length of overlap on the other bank = (1/2) * 50 meters = 25 meters
Finally, let's add the lengths of the overlapping sections to get the total length of the bridge:
Total length of the bridge = Length of overlap on one bank + Length of overlap on the other bank
Total length of the bridge = (50/3) meters + 25 meters
To add the lengths together, we need to find a common denominator:
Total length of the bridge = (50/3) meters + (25 * 3/3) meters
Total length of the bridge = (50/3) meters + 75/3 meters
Total length of the bridge = (50 + 75)/3 meters
Total length of the bridge = 125/3 meters
Now, let's simplify the fraction:
Total length of the bridge = 41 2/3 meters
Since the question asks for the answer in meters, we can say that the total length of the bridge is approximately 41.67 meters.
The closest answer choice is A. 100 meters.