標題:
F.2 Ratio and Rate (10marks)
發問:
1) Which is the lower rate: 630 l/h or 150 c.c./s ?2) Given a rectangle of dimensions 3cm4cm. If this rectangle is a scale drawing to a scale of 1:250, find its actual area in ㎡.3) A car is parked in a car-park from 7:45 a.m. to 4:30 p.m. on the same day. Find a) the total time for which the car is... 顯示更多 1) Which is the lower rate: 630 l/h or 150 c.c./s ? 2) Given a rectangle of dimensions 3cm4cm. If this rectangle is a scale drawing to a scale of 1:250, find its actual area in ㎡. 3) A car is parked in a car-park from 7:45 a.m. to 4:30 p.m. on the same day. Find a) the total time for which the car is parked, b) the parking fee if the rate of charges is $12.5 for the first hour and $5 for each half hour or part of a half hour thereof. 4) Car A travels at 54 km/h and car B travels at 24 m/s. Find the ratio of the speed of car A to that of car B.
最佳解答:
1) 1L = 1,000cc and 1h = 60 minutes = (60 X 60)s = 3600 s 630 L / h = 630 L / 1 h = ( 630 X 1000 mL ) / ( 1 X 60 X 60 ) s = ( 630 X 1000 cc ) / ( 1 X 60 X 60 ) s = 630000 cc / 3600 s = 175 cc / s ∴the lower rate is 175 cc / s 2)the actual area of the rectangle = length X wide = (3 cm X 250) X (4 cm X 250) = 750 cm X 1000 cm = 7.5 m X 10 m = 750 m2 Another method： the area on the map = (3 X 4)cm2 = 12cm2 this rectangle is a scale to a scale of 1:250 Hence the area of ratio = 12：2502 = 1：62500 the actual area of the rectangle = 12 X 2502 = 12 X 62500 = 750000cm2 = (750000 / 10000)m2 = 75m2 Remark：1m = 100cm 1m2 = 1002cm2 = 10000m2 3a)the parking time from 7:45 a.m. to 3:45 p.m. = 8 hours parking time from 15:45p.m. to 16:30p.m. = 45 mins The total time for which the car is parked is 8 hours and 45 minutes b)First hour spent $12.5 (From 7:45a.m. to 8:45a.m.) the remaining time is 7 hours and 45 minutes and 1 part of a half hour = 7 + (45 / 60) ←( 1h = 60mins ) = 7.75 hours = 7.75 X 2 + 0.5 ←(1 part of a half hour) = 16 half-hour periods The parking fee is therefore $12.5 + 16 X $5 = $92.5 4)You should change km/h to m/s as they have the same unit. the speed of car A = 54km/h = (54 X 1000)m / (1 X 60 X 60)s = 54000m / 3600s = 15 m/s speed of car A：speed of car B = 15m/s：24m/s = 5：8 Remark：1h = 60 X 60 = 3600s and 1km = 1000m
F.2 Ratio and Rate (10marks)
發問:
1) Which is the lower rate: 630 l/h or 150 c.c./s ?2) Given a rectangle of dimensions 3cm4cm. If this rectangle is a scale drawing to a scale of 1:250, find its actual area in ㎡.3) A car is parked in a car-park from 7:45 a.m. to 4:30 p.m. on the same day. Find a) the total time for which the car is... 顯示更多 1) Which is the lower rate: 630 l/h or 150 c.c./s ? 2) Given a rectangle of dimensions 3cm4cm. If this rectangle is a scale drawing to a scale of 1:250, find its actual area in ㎡. 3) A car is parked in a car-park from 7:45 a.m. to 4:30 p.m. on the same day. Find a) the total time for which the car is parked, b) the parking fee if the rate of charges is $12.5 for the first hour and $5 for each half hour or part of a half hour thereof. 4) Car A travels at 54 km/h and car B travels at 24 m/s. Find the ratio of the speed of car A to that of car B.
最佳解答:
1) 1L = 1,000cc and 1h = 60 minutes = (60 X 60)s = 3600 s 630 L / h = 630 L / 1 h = ( 630 X 1000 mL ) / ( 1 X 60 X 60 ) s = ( 630 X 1000 cc ) / ( 1 X 60 X 60 ) s = 630000 cc / 3600 s = 175 cc / s ∴the lower rate is 175 cc / s 2)the actual area of the rectangle = length X wide = (3 cm X 250) X (4 cm X 250) = 750 cm X 1000 cm = 7.5 m X 10 m = 750 m2 Another method： the area on the map = (3 X 4)cm2 = 12cm2 this rectangle is a scale to a scale of 1:250 Hence the area of ratio = 12：2502 = 1：62500 the actual area of the rectangle = 12 X 2502 = 12 X 62500 = 750000cm2 = (750000 / 10000)m2 = 75m2 Remark：1m = 100cm 1m2 = 1002cm2 = 10000m2 3a)the parking time from 7:45 a.m. to 3:45 p.m. = 8 hours parking time from 15:45p.m. to 16:30p.m. = 45 mins The total time for which the car is parked is 8 hours and 45 minutes b)First hour spent $12.5 (From 7:45a.m. to 8:45a.m.) the remaining time is 7 hours and 45 minutes and 1 part of a half hour = 7 + (45 / 60) ←( 1h = 60mins ) = 7.75 hours = 7.75 X 2 + 0.5 ←(1 part of a half hour) = 16 half-hour periods The parking fee is therefore $12.5 + 16 X $5 = $92.5 4)You should change km/h to m/s as they have the same unit. the speed of car A = 54km/h = (54 X 1000)m / (1 X 60 X 60)s = 54000m / 3600s = 15 m/s speed of car A：speed of car B = 15m/s：24m/s = 5：8 Remark：1h = 60 X 60 = 3600s and 1km = 1000m
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