# Two motorists, A and B, started their journey from two towns 240km apart at 0830. They wanted to meet each other at 10 00. If motorist A had increased his speed by 10km/h but motorist B halved his...

Two motorists, A and B, started their journey from two towns 240km apart at 0830. They wanted to meet each other at 10 00. If motorist A had increased his speed by 10km/h but motorist B halved his speed, they would be late for their appointment by 30minutes. Find their original speeds.(Hint: When they meet, the total distance travelled is 240km.)

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### 1 Answer

Speed is distance traveled over time i.e. ` ` . Since there are two motorists traveling in opposite directions their combined speed is the sum of their respective speeds and we know the distance traveled is 240 km and the time is 1.5 h. Therefore we get

` `

Now we consider what happens if A increases the speed by 10km/h an B halves his speed (time is now 2h).

`v_A+10+v_B/2=240/2`

` `Now we have system of two equations with 2 unknowns.

From first equation we get

`v_A=160-v_B`

So we plug that into second equation.

`160-v_B+10+v_B/2=120`

`320-2v_B+20+v_B=240`

`-v_B=-100`

`v_B=100`

Now we plug this value into the substitution.

`v_A=160-100`

`v_A=60`

**Original speeds of motorists A and B are 60 km/h and 100 km/h respectively.**