Q1 A car travels from town P to town Q at a constant speed.When it increases its speed by 20%,the journey from P to Q takes 1 hour less than its usual time.When it travels at its usual speed for 100 km before increasing its speed by 30%,the journey also takes 1 hour less than usual.Find the distance between the two towns.
Q2 Two cars race around a circular track at constant speeds starting at the same point. If they travel in opposite directions, then they meet every 30 seconds. If they travel in the same direction, then they meet every two minutes. If the track is 1800m long,what is the speed of each car?
Q3 Alan increases his speed by 25km/h. When he does so, the time taken to travel on a 25km trip decreases by 10 mins. What is his initial speed?
Originally posted by Chocolate Cake:Q1 A car travels from town P to town Q at a constant speed.When it increases its speed by 20%,the journey from P to Q takes 1 hour less than its usual time.When it travels at its usual speed for 100 km before increasing its speed by 30%,the journey also takes 1 hour less than usual.Find the distance between the two towns.
Q2 Two cars race around a circular track at constant speeds starting at the same point. If they travel in opposite directions, then they meet every 30 seconds. If they travel in the same direction, then they meet every two minutes. If the track is 1800m long,what is the speed of each car?
Q3 Alan increases his speed by 25km/h. When he does so, the time taken to travel on a 25km trip decreases by 10 mins. What is his initial speed?
u sure p6 one arh?
i use algebra also very hard to solve leh
for q1, distance = 360km, for q2, one car is 37.5m/s and the other one is 22.5m/s. for q3, the start speed is 50km/h.
Qn taken from Ai Tong School 2008 P6 SA1 - Q42
Ali and Dave cycled from Town A to Town B at 12 km/h and 10 km/h respectively.Ali left Town A at 8.30 am and arrived at Town B at 9 am. When Ali arrived at Town B, Dave was 1.5 km away from Town B. What time did Dave leave Town A ? (4 marks)
Thanks.
Originally posted by Chocolate Cake:Qn taken from Ai Tong School 2008 P6 SA1 - Q42
Ali and Dave cycled from Town A to Town B at 12 km/h and 10 km/h respectively.Ali left Town A at 8.30 am and arrived at Town B at 9 am. When Ali arrived at Town B, Dave was 1.5 km away from Town B. What time did Dave leave Town A ? (4 marks)
Thanks.
Dist between the towns is 12 X 0.5 = 6km
Dist Dave travelled is 6-1.5 = 4.5km
Time Dave travelled = 4.5/10 = 0.45hr = 27mins
Therefore, Dave left Town A at 8.33am
Q5 Car A and Car B are travelling towards Town Y from Town X. Both cars left Town X at different times. At 1030, Car A has travelled 3/8 of the distance between Town X and Town Y, while Car B has travelled 2/9 of the distance between Town X and Town Y. At 1035, the distance travelled by Car B is 3/5 of the distance travelled by Car A. If the speed of both cars are the same, find the time Car B reaches Town.
Q6 Sally arrives at the station at the same time every day. Her husband drives from home to the station to pick her up. They always arrive back at their house at the same time every day, driving at the same speed. One day she arrives at the station one hour early and starts to walk home. Her husband meets her along the road and they drive home together. They arrived home 10 minutes earlier than usual. Assuming all speeds of walking and driving are constant and all transfers are immediate, how long had the woman been walking when her husband met her? (answer in minutes)
Originally posted by Chocolate Cake:Q5 Car A and Car B are travelling towards Town Y from Town X. Both cars left Town X at different times. At 1030, Car A has travelled 3/8 of the distance between Town X and Town Y, while Car B has travelled 2/9 of the distance between Town X and Town Y. At 1035, the distance travelled by Car B is 3/5 of the distance travelled by Car A. If the speed of both cars are the same, find the time Car B reaches Town.
Q6 Sally arrives at the station at the same time every day. Her husband drives from home to the station to pick her up. They always arrive back at their house at the same time every day, driving at the same speed. One day she arrives at the station one hour early and starts to walk home. Her husband meets her along the road and they drive home together. They arrived home 10 minutes earlier than usual. Assuming all speeds of walking and driving are constant and all transfers are immediate, how long had the woman been walking when her husband met her? (answer in minutes)
Q5.
Both cars have the same speed.
At 1030, car A = 3/8 of distance = 54/144 of distance
and car B = 2/9 of distance = 32/144 of distance
At 1035, x/144 of the distance has been travelled, hence 5 mins = x/144 of distance.
(32+x)/(54+x) = 3/5
= > x = 1
= > 5 mins = 1/144 of total distance.
Distance left for car B at 1030 = 1 - 32/144 = 112/144 of total distance
Amount of time needed for car B
= [( 112/144 ) / ( 1/144 )] X 5 mins
= 560 mins
Time car B reaches Town Y
= 1030 + 560 mins
= 1030 + 9 hours 20 mins
= 1950 = 7.50 pm
Q6.
Interesting question, if you know what you are doing, it is easy, if you don't, it is hard.
Time saved by husband = 10 mins
= > Distance between the point when husband meet wife and the station
= 10/2 = 5 mins
Time wife arrived earlier = 1 hour = 60 mins
Time wife walked = 60 mins - 5 mins = 55 mins