man covered a certain distance at some speed had he moved 3 km/hr faster he would have taken 40 minutes less If he had moved 2 km/hr slower he would have taken 40 minutes more The distance ( in km)
Answers
Answer:
Answer:
The distance and speed are 40 km and 12 km/hr respectively.
Step-by-step explanation:
Let us assume that the certain distance and speed be x and y respectively.
Formula: Time = Distance/Speed
According to question:
He moved 3 km/hr faster he would have taken 40 minutes less,
x/y - x/(y + 3) = 40/60 [1 minute = 1/60 hour]
→ (xy + 3x - xy)/(y² + 3y) = 2/3
→ 3x/(y² + 3y) = 2/3
→ 9x = 2y² + 6y ___________(i)
If he had moved 2 km/hr slower he would have taken 40 minutes more,
x/(y - 2) - x/y = 40/60
→ (xy - xy + 2x)/(y² - 2y) = 2/3
→ 2x/(y² - 2y) = 2/3
→ 3x = y² - 2y ___________(ii)
On dividing equation (i) by equation (ii):
9x/3x = (2y² + 6y)/(y² - 2y)
→ 3 = y(2y + 6)/y(y - 2)
→ 3(y - 2) = 2y + 6
→ 3y - 6 = 2y + 6
→ y = 12
Substituting the value of y in equation (ii):
3x = (12)² - 2 × 12
Answer:
40km/ hr
Step-by-step explanation:
Let the distance = x km and usual rate = y km/hr Then
y
x
−
y+3
x
=
60
40
⇒
y(y+3)
x(y+3)−xy
=
3
2
⇒
y(y+3)
3x
=
3
2
⇒2y(y+3)=9x...............(i)
and
y−2
x
−
y
x
=
60
40
⇒
y(y−2)
xy−x(y−2)
=
3
2
⇒
y(y−2)
2x
=
3
2
⇒y(y−2)=3x...............(ii)
On dividing eqn (i) by eqn (ii) we get
y−2
2(y+3)
=3⇒2y+6=3y−6⇒y=12
∴ Putting the value of y in (i) we get 2 x 12 x 15 = 9x ⇒ x = 40 km/hr