Two buses start from the opposite points of a main road, 150kms apart. The first bus runs for 25kms and takes a right turn and then runs for 15 kms. It then turns left and runs for another 25 kms and takes the direction back to reach the mai road. In the meantime, due to a minor breakdown, the other bus has run only 35 kms along the main road. What would be the distance between the two buses at this point? Group of answer choices 75kms 65kms 85kms 80kms
Question
Two buses start from the opposite points of a main road, 150kms apart. The first bus runs for 25kms and takes a right turn and then runs for 15 kms. It then turns left and runs for another 25 kms and takes the direction back to reach the mai road. In the meantime, due to a minor breakdown, the other bus has run only 35 kms along the main road. What would be the distance between the two buses at this point?
Group of answer choices
75kms
65kms
85kms
80kms
Solution
The first bus runs for 25 kms along the main road, then takes a right turn and runs for 15 kms, then turns left and runs for another 25 kms. This means that the first bus is now 25 kms away from the main road (15 kms to the right and 25 kms forward, forming a right triangle with the main road).
The other bus has run 35 kms along the main road.
The distance between the two buses along the main road is the initial distance of 150 kms minus the distances they have run along the main road. This is 150 kms - 25 kms (for the first bus) - 35 kms (for the other bus) = 90 kms.
However, the first bus is also 25 kms away from the main road. So, the actual distance between the two buses is the hypotenuse of a right triangle with sides of 90 kms (along the main road) and 25 kms (away from the main road).
Using the Pythagorean theorem, the distance between the two buses is sqrt(90^2 + 25^2) = sqrt(8100 + 625) = sqrt(8725) = 93.4 kms.
However, this is not one of the options. Let's check the calculations again.
The mistake is in the calculation of the distance between the two buses along the main road. The first bus has run 25 kms along the main road, not 35 kms. So, the distance between the two buses along the main road is 150 kms - 25 kms (for the first bus) - 35 kms (for the other bus) = 90 kms.
The actual distance between the two buses is the hypotenuse of a right triangle with sides of 90 kms (along the main road) and 25 kms (away from the main road).
Using the Pythagorean theorem, the distance between the two buses is sqrt(90^2 + 25^2) = sqrt(8100 + 625) = sqrt(8725) = 93.4 kms.
So, the correct answer is 93.4 kms, which is closest to 95 kms. However, this is not one of the options. The closest option is 85kms.
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