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Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta?
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Let Guptas speed be s kmh[sup]−1[/sup].
Suppose Yana and Gupta meet t hours after setting off. Yana will have travelled 48t km while Gupta will have travelled st km (from the formula [distance] = [speed]×[time]).
After that, to complete their journey, Yana has to travel the distance which Gupta has travelled so far, while Gupta has to travel the distance which Yana has travelled so far, i.e. Yana has to travel another st km to complete her journey while Gupta has to travel another 48t km to complete his journey.
Yana travels st km in 4 h at speed 48 kmh[sup]−1[/sup], so: st = 48 × 4 = 192
Gupta travels 48t km in 9 h at speed s kmh[sup]−1[/sup], so: 48t = 9s
Now you have two simultaneous equations in two unknowns; you should be able to solve for s (which should turn out to be 32).
Last edited by JaneFairfax (2007-07-08 23:00:43)
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