A car travels 300 km at a uniform rate. if the speed of the car had been 5 km/hr more, the journey would have taken 2 hr less. what is the speed of the car?
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Let speed be 's ', time be 't ' and distance be 'd ' t, t = d / s t = 300 / s ,
d = (s + 5)(t -2) => d = (s+5)(300/s-2) {t=300/s} => 300s = (s+5)s(300/s-2) [multiplyning both sides with s]we get = > 300s = (s+5)(300 - 2s)=> 300s = 300s - 2s2 +1500 - 10s => 300s = 300s - 2s2 + 1500 - 10s=> 0 = -2s2 +1500 - 10s=> 0 = 2s2 +10s - 1500 [multiplying both sides -1 ]=> 0 = 2s2 +60s - 50s - 1500=> 0 = 2s(s + 30) -50(s + 30)=> 0 = (2s - 50)(s + 30)=> s = 25, -30 Since, speed cannot be negative, we take speed 25Km/h.
d = (s + 5)(t -2) => d = (s+5)(300/s-2) {t=300/s} => 300s = (s+5)s(300/s-2) [multiplyning both sides with s]we get = > 300s = (s+5)(300 - 2s)=> 300s = 300s - 2s2 +1500 - 10s => 300s = 300s - 2s2 + 1500 - 10s=> 0 = -2s2 +1500 - 10s=> 0 = 2s2 +10s - 1500 [multiplying both sides -1 ]=> 0 = 2s2 +60s - 50s - 1500=> 0 = 2s(s + 30) -50(s + 30)=> 0 = (2s - 50)(s + 30)=> s = 25, -30 Since, speed cannot be negative, we take speed 25Km/h.
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