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A motorcyclist leaves City A and rides at a constant speed towards City B, which is 225 km away. After 1.5 hours, the motorcyclist stops a half an hour lunch. To reach City B on time, the motorcyclist increases his speed after lunch by 10km/hour. Find the motorcyclists original speed

Respuesta :

Answer:

50 km/hr

Step-by-step explanation:

OK, this is how I solved this problem.

Let r = original rate of speed

     t = time after the stop to finish the trip

Time for trip without stopping is 225/r

(1)     1.5 + .5 + t = 225/r      This is a time equation

(2)    1.5r + t(r + 10) = 225     This is a distance equation

(1)       2 + t = 225/r            (2)      1.5r + tr + 10t = 225

         2r + tr = 225

                tr = 225 - 2r                 1.5r + 225 - 2r + 10(225/r - 2) = 225

                t = 225/r - 2

                                                   -.5r + 225 + 2250/r - 20 = 225

                                                     -5r + 2250 + 22500/r - 200 = 2250

                                                     -5r^2 + 2250r + 22500 - 200r = 2250r

                                                       5r^2 + 200r - 22500 = 0

                                                       5(r^ + 40r - 4500) = 0

                                                           5(r - 50)(r + 90) = 0

                                                                 r = 50   or    r = -90

The rate cannot be negative, so the original speed 50 km/hr

This not an easy problem and I hope you were able to follow my work

Answer:50km hope that helped pls mark me brainliest :))

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