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發問:
A lorry departs from place A and travels at a speed of 40 km/h in the first hour. Then its speed is increased by 3km/h for each hour thereafter. A sports car which is behind the lorry and 45 km from place A sets out in the same direction as the lorry at the same time. It travels at a speed of... 顯示更多 A lorry departs from place A and travels at a speed of 40 km/h in the first hour. Then its speed is increased by 3km/h for each hour thereafter. A sports car which is behind the lorry and 45 km from place A sets out in the same direction as the lorry at the same time. It travels at a speed of 45km/h in the first hour and its speed is increaed by 4km/h for each hour thereafter. Suppose the sports car catches up with the lorry after n hours. a. Express (i) the distance travelled by the lorry in terms of n (ii) the distance travelled by the sports car in terms of n b. Find the value of n would you please show your steps clearly, thank you very much! i appreciate your prompt answer !! >W< THank! 更新: sorry , i want to add something Ans ai) n(3n+77)/2 aii) n(2n+43) b. n=6 i want to see the steps.. thank you very much @W@
最佳解答:
Let x be the distance from A which the lorry travels to the point where the car catches the lorry. Let t be time taken for the car catching lorry (a)(i) distance of lorry travel: x = (40)(1) + 43(n-1) = 43n - 3 (a)(ii) distance of car travel: x+45 = 45(1) + 49(n-1) => x = 49n - 49 (b) sub the equation at part (a)(i) into the equation at part (a)(ii) 43n - 3 = 49n - 49 6n = 46 n = 7.667 hr 2009-04-10 23:01:19 補充： Revised answer (a) x = 40(1) + (40+3) (1) + (40+3x2)(1) + ...+(40+3x(n-1))(1) x = [2(40) + (n-1)(3)]n/2 = n(3n+77)/2 2009-04-10 23:04:14 補充： Revised answer (a)(ii) x + 45 = 45 + (45+4)(1) +(45+4x2)(1)+...+ (45+4x(n-1)) x + 45 = [2(45) + (n-1)(4)]n/2 x + 45 = n(43 + 2n) 2009-04-10 23:06:51 補充： Revised answer (b) sub equation (a)(i) into equation (a)(ii): n(3n+77)/2 + 45 = n(43+2n) 3n^2 + 77n + 90 = 86n + 4n^2 n^2 + 9n - 90 = 0 (n - 6) (n + 15) = 0 n = 6 or n= -15 (rejected) n = 6 hours
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Maths F5 sequences Help!! >W發問:
A lorry departs from place A and travels at a speed of 40 km/h in the first hour. Then its speed is increased by 3km/h for each hour thereafter. A sports car which is behind the lorry and 45 km from place A sets out in the same direction as the lorry at the same time. It travels at a speed of... 顯示更多 A lorry departs from place A and travels at a speed of 40 km/h in the first hour. Then its speed is increased by 3km/h for each hour thereafter. A sports car which is behind the lorry and 45 km from place A sets out in the same direction as the lorry at the same time. It travels at a speed of 45km/h in the first hour and its speed is increaed by 4km/h for each hour thereafter. Suppose the sports car catches up with the lorry after n hours. a. Express (i) the distance travelled by the lorry in terms of n (ii) the distance travelled by the sports car in terms of n b. Find the value of n would you please show your steps clearly, thank you very much! i appreciate your prompt answer !! >W< THank! 更新: sorry , i want to add something Ans ai) n(3n+77)/2 aii) n(2n+43) b. n=6 i want to see the steps.. thank you very much @W@
最佳解答:
Let x be the distance from A which the lorry travels to the point where the car catches the lorry. Let t be time taken for the car catching lorry (a)(i) distance of lorry travel: x = (40)(1) + 43(n-1) = 43n - 3 (a)(ii) distance of car travel: x+45 = 45(1) + 49(n-1) => x = 49n - 49 (b) sub the equation at part (a)(i) into the equation at part (a)(ii) 43n - 3 = 49n - 49 6n = 46 n = 7.667 hr 2009-04-10 23:01:19 補充： Revised answer (a) x = 40(1) + (40+3) (1) + (40+3x2)(1) + ...+(40+3x(n-1))(1) x = [2(40) + (n-1)(3)]n/2 = n(3n+77)/2 2009-04-10 23:04:14 補充： Revised answer (a)(ii) x + 45 = 45 + (45+4)(1) +(45+4x2)(1)+...+ (45+4x(n-1)) x + 45 = [2(45) + (n-1)(4)]n/2 x + 45 = n(43 + 2n) 2009-04-10 23:06:51 補充： Revised answer (b) sub equation (a)(i) into equation (a)(ii): n(3n+77)/2 + 45 = n(43+2n) 3n^2 + 77n + 90 = 86n + 4n^2 n^2 + 9n - 90 = 0 (n - 6) (n + 15) = 0 n = 6 or n= -15 (rejected) n = 6 hours
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