SOLUTION: Mr Li travel by taxis or bus to work Distance is 25 km and the speed of taxis is v km/hr The taxis travel 20 km/hr faster than the bus My solution step To find time taken by

Algebra ->  Expressions-with-variables -> SOLUTION: Mr Li travel by taxis or bus to work Distance is 25 km and the speed of taxis is v km/hr The taxis travel 20 km/hr faster than the bus My solution step To find time taken by      Log On


   

Question 1024273: Mr Li travel by taxis or bus to work
Distance is 25 km and the speed of taxis is v km/hr
The taxis travel 20 km/hr faster than the bus
My solution step
To find time taken by taxis and by bus. My confusion is what is the speed for bus as the question did not give.?..?......the question only give taxis speed
1. Time taken by taxis. = distance/ speed = 25/ (v+20). Because 20 km/hr speed faster than bus

2. Time taken for bus. = 25/v
3 given bus is 15 min use more than taxis , proof equation v^2-20v-2000=0
Pls help, thank you
Hendor
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Mr Li travel by taxis or bus to work
Distance is 25 km and the speed of taxis is v km/hr
The taxis travel 20 km/hr faster than the bus
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Time for the taxi = 25/v hours.
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Time for the bus = 25/(v - 20) hours.
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25/(v-20) - 25/v = 0.25 hours
100/(v-20) - 100/v = 1
100v - 100(v-20) = v(v-20)
100v -100v + 2000 = v^2 - 20v
v^2 - 20v - 2000 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-20x%2B-2000+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A1%2A-2000=8400.

Discriminant d=8400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+8400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+8400+%29%29%2F2%5C1+=+55.8257569495584
x%5B2%5D+=+%28-%28-20%29-sqrt%28+8400+%29%29%2F2%5C1+=+-35.8257569495584

Quadratic expression 1x%5E2%2B-20x%2B-2000 can be factored:
1x%5E2%2B-20x%2B-2000+=+%28x-55.8257569495584%29%2A%28x--35.8257569495584%29
Again, the answer is: 55.8257569495584, -35.8257569495584. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B-2000+%29

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v =~ 55.8 km/hr (taxi)
v - 20 =~ 35.8 km/hr (bus)