Question

Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a
train arriving there from B. He must reach C at least 15 minutes before the arrival of the
train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of
50 km per hour. It is known that C is located between west and northwest of B, with BC at
60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The
latest time by which Rahim must leave A and still catch the train is closest to
1) 6:15 am 2) 6:30 am 3) 6:45 am 4) 7:00 am 5) 7:15 am​

Answer 1

Step-by-step explanation:

C should be in the Southwest Of A

BCA is a (60-90-30) triangle. hence, BC= 500/2=250 Km and AC= 500*

Time taken by train to reach C= 250/50= 5hr

Train will arrive C at 1 PM

hence, Rahim must arrive C latest by 12:45 PM

Time taken by Rahim to reach C= = 6.18 hrs =~ 6 hrs 12 mins

The latest time by which Rahim must leave A and still catch the train= 1245 - 612 =~ 0633 hrs or 6:33 AM