AMCAT Speed, Time and Distance Quiz-1

Correct Option: 18
By applying a formula,

Speed = Distance/ Time

Speed = [ 1250 / 250 ] m/sec = 5m/sec

= [ 5 × 18/5 ] km/hr ⇒ 18 km / hr.

Solution:
Let distance travelled = x km
\frac{x}{40} – \frac{x}{60} = 1
=> \frac{20x}{2400} = 1
=> x = 120 km

Answer: 2.8 h
S: Total running distance in four weeks = (20 x 500) + (4 x 1000) = 14000m = 14 km
Time = \frac{14}{5} = 2.8 hours

Explanation- Say speed of Jake is J and Speed of Paul is P.
Given J + P = 7 ……. (Eq.1)
Time = Distance/speed.
⇒ Time taken by Jake to cover 24 km = 24/J hours
⇒ Time taken by Paul to cover 24 km = 24/P hours
Given, sum of times = 14 hours.
⇒ (24/J) + (24/P) = 14
⇒ (1/J) + (1/P) = 7/12
Using Eq.1,
⇒ (J + P)/(JP) = 7/12
⇒ J × P = 12
∴ (J – P)2 = (J + P)2 – 4JP = 72 – 4 × 12 = 1
⇒ (J – P) = 1 ……. (Eq.2)
Eq.1 + Eq.2
⇒ 2J = 8
⇒ J = 4 km/h

Correct Option: C
1 Bike + 1 Walk = 5 hrs 45 mins

2 Bike = 3 hrs 45 mins

Hence 1 way Bike journey takes 1 hrs 52.5 mins

So, 1 way walk should take (5 hr 45 mins) – (1 hrs 52.5 mins) = 3 hr 52.5 mins

2-way walk would take: 3 hr 52.5 mins 2 = 7 hr 45 mins

Solution:
Time taken in walking one way and riding other way = 10 hours
Time taken in riding both the ways = 5 hours
Time taken in walking one way * 2 = 20 hours – 5 hours = 15 hours

Answer: 40 km/hr
S: Using Short Cut Method:
Let Suppose x and y be two given speeds,
x= 30 km/h , y= 60km/h
Now, Average speed = 2xy / ( x+y )
=\frac{2\times30\times60}{30+60}
Average Speed = 40 km / h.

Explanation- Say after X hours Jeremy started, Pranjal would be 3 km ahead of Jeremy.
Distance = Speed × Time
Distance traveled by Pranjal in X hours = 6 × X km
Distance traveled by Jeremy by this time = 9 × (X – 1.5) [Pranjal started 1.5 hours late]
Given, by this time Pranjal is 3 km a head of Jeremy
⇒ 9 × (X - 1.5) = 6X + 3
⇒ 3X = 3 + 13.5 = 16.5
⇒ X = 5.5 hours
So the time is 12:00 pm + 5.5 hours = 17:30 pm

Correct Option: 40 min
Let the distance be x, then,

(Time taken to walk x km) + (Time taken to ride x km) = 58 min.

⇒ (Time taken to walk 2x km) + (Time taken to ride 2x km) = 116 min.

But, time taken to walk both ways 2x km = 76 min.

So, Time to ride 2x km = (116 - 76) min ⇒ 40 min.

Solution:
x + y = \frac{(5 * 60)}{10} = 30 ——–(1)
and
x – y = \frac{(5 * 60)}{12} = 25 ———(2)
From (1) and (2) , we get
x + y – x + y = 30 – 25 = 5
=> y = 2.5 \frac{km}{hr}