A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find:
a) The distance the car has covered.
b) The time that took it to get from C to B.
Choose the correct choice from the following answers.
A) 223
B) 277
C) 116
D) 268
E) 281
From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. So we have to consider both cases.   1st case. The stop was planned. Let us consider only the trip from C to B, and let xx be the number of hours the driver spent on this trip.   Then the distance from C to B is S=40⋅xS=40⋅x km. If the driver could use the initial route, it would take him x−3060=x−12x−3060=x−12 hours to drive from C to B. The distance from C to B according to the initially itinerary was (x−12)⋅32(x−12)⋅32 km, and this distance is 2828 km shorter than 40⋅x40⋅x km. Then we have the equation   (x−1/2)⋅32+28=40x(x−1/2)⋅32+28=40x   32x−16+28=40x32x−16+28=40x   −8x=−12−8x=−12   8x=128x=12   x=128x=128   x=148=112=13060=x=148=112=13060= 1 hr 30 min.   So, the car covered the distance between C and B in 1 hour and 30 min.   The distance from A to B is 3⋅32+128⋅40=96+60=1563⋅32+128⋅40=96+60= 
<gadget id="calculator">96+60</gadget>
<output>156</output>
156 km.   2nd case. The driver did not plan the stop at C. Suppose it took xx hours for him to get from C to B. Then the distance is S=40⋅xS=40⋅x km. It took x−3060−1560=x−4560=x−34x−3060−1560=x−4560=x−34 h to drive from C to B. The distance from C to B is 32(x−34)32(x−34) km, which is 2828 km shorter than 40⋅x40⋅x, i.e.   32(x−34)+28=40x32(x−34)+28=40x   32x−24+28=40x32x−24+28=40x   4=8x4=8x   x=12hr⋅x=30min.x=12hr⋅x=30min. Then the time of the trip from C to B was 30 min. The distance covered equals 3⋅32+12⋅40=96+20= 
<gadget id="calculator">96+20</gadget>
<output>116</output>
116km3⋅32+12⋅40=96+20= 
<gadget id="calculator">96+20</gadget>
<output>116</output>
116km.   Answer:116
<result>C</result>
A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find:
a) The distance the car has covered.
b) The time that took it to get from C to B.