A race with three cars

Algebra Level 2

Three cars A, B and C standing at the same starting line. A start the first with 30km/h. Two minutes later, B start going with 40km/h. Three minutes after B started, C also start with a speed of 60km/h. When B catch A at a point, A increase the speed by 15km/h.

When C catch A at a point, how many kilometers will be it far from the starting point?

The answer is 7.

2 solutions

Rohit Sachdeva
Apr 18, 2015

A is 0.5km/min, B is 0.667km/min & C is 1km/min

After 2 mins A has covered 1km & B is at start.

It will take (1km)/(0.667-0.5km/min)=6mins for B to catch A from this point (or 8mins from start)

Distance they would have covered is 8x0.5 = 6x0.667 = 4km

Now 8mins for C means 5mins of waiting + 3mins of driving at 1km/min=3km

Hence Now A & C are 1km apart with A speed as 0.75km/min (increased)

Time taken for C to catch up with A = 1/(1-0.75) = 4min

Distance by C in 4min = 4km

(Note that distance by A in 4min = 3km)

So both are 7km away from start point

Venture Hi
Apr 17, 2015

Draw a diagram to help visualise where A, B and C are at each time frame.

At t=2, A is 1 km from starting point. At t=5, A is 2.5km from starting point and B is 2km from starting point. At this point in time, C is still at starting point.

Whem B catch A, A has travelled (x)km and B has travelled (0.5+x) km. Therefore, (0.5+x)/40=x/30. Solve for x. x=2.5 km. A and B meets at 4km mark from starting point.

Then time it took for B to catch up is (2km)/40km/h)= 1/20 hr or 3 minutes.

In this time span of 3 minutes, C has travelled 60*(3/60)= 3 km

When C caught up with A who is now going at 45km/h, A would have travelled another x km and C (1+x) km. Therefore, (1+x)/60=x/45. solve for x. x= 3km

So, total distance travelled by C is 3+1+3= $\boxed{7}$

A race with three cars

The answer is 7.

2 solutions

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