Masha biked 20 km 20 minutes faster than Dasha biked 20 km. Find the speed of each cyclist if one biked 2 km/h faster than the other.

Step-by-step explanation:

Speed is the distance traveled by a body with respect to time.

Speed = Distance/Time

Distance = speed * time

For Dasha;

Distance travelled = 20km

Time travelled is not known, so we say x

Distance = speed* x

20 = S * x 1

For Masha;

Distance travelled = 20km

If he travelled 20min faster than Dasha, time travelled = 20/60 + x

Distance = speed* (1/3 + x)

20 = S * (1/3 + x) 2

Equating 1 and 2 since they are of the same distance;

Sx = S(1/3+x)

Also if one biked 2 km/h faster than the other.

(S+2)x = S(1/3 + x)

On expansion;

Sx + 2x = S/3 + Sx

2x = S/3

Given the speed S to be 2km/h

2x = 2/3

x = 1/2

Time traveled by Dasha will be 1/2 hr wile Time traveled by Masha will be (1/3 + 1/2) = 5/6 hr

Speed = Distance/time

Speed of Masha = 20/(5/6)

Speed of Masha = 20 * 6/5

Speed of Masha = 24km/hr.

Speed of Dasha = 20/(1/2)

Speed of Dasha = 20 * 2/1

Speed of Dasha = 40km/hr

Answers are 12km/h and 10km/h

Step-by-step explanation:

Rsm 2021

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