# Linear Equation in Two Variables Distance Problems

This worksheet is based on linear equation in two variables distance problems.In linear equation in two variables distance problems you have to use two variables and you can solve using any method such as substitution or elimination.1. A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55km downstream. Determine the speed of the stream and that of boat in still water. (Ans)

2. Tara can row downstream 20km in 2 hours, and upstream 4km in 2 hours. Find her speed of rowing in still water and the speed of the current. (Ans)

3. A sailor goes 8 km downstream in 40 minutes and comes back in 1 hour. Determine the speed of the sailor in still water and the speed of current. (Ans)

4. Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other they meet in one hour. What are their respective speeds? (Ans)

5. Amy travelled 300km by train and 200km by taxi, it took him 5 hours 30 minutes. But if he travels 260km by train and 240km by taxi he takes6 minutes longer. Find the speed of train and taxi. (Ans)

6. A man travels 600 km partly by train and partly by car. If he covers 400km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200km by train and rest by car, he takes 30 minutes longer. Find the speed of train and that of car. (Ans)

7. The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10km, the charge paid is $75 and for a journey of 15km, the charge paid is $110. What will a person have to pay for traveling a distance of 25km? (Ans)

8. A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class from Michigan to Massachusetts costs $216 and one full and one half reserved first class tickets cost $327. What is the basic first class full fare and what is the reservation charge? . (Ans)

9. A man walks certain distance with certain speed. If he walks 1/2km/hr faster, he takes 1hr less. But if he walks 1km/hr slower, he takes 3more hours. Find the distance covered by the man and his original rate of walking. . (Ans)

10. A car goes uphill at the rate of 30km an hour and downhill at the rate of 50km an hour after 15hours it has covered 650km. How long did it go downhill and uphill respectively? . (Ans)

11. Ronnie travels 300km to her home partly by train and partly by bus. She takes 4 hours if she travels 60km by train and the remaining by bus. If she travels 100km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and bus separately. . (Ans)

12. A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster it would have 8 hours less than the scheduled time, and if the train were slower by 6km/hr,it would have taken 12 hours more than the scheduled time. Find the length of the journey. . (Ans)

13. If you were to travel by metro the fare for the first kilometer is different from the rate per kilometer for the remaining distance. The total fare for a distance of 20m is $37.70 and that for a distance of 26km is $48.50. find the auto fare for the first kilometer and for each successive kilometer. (Ans)

14. A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4 hours less than the scheduled time. And is the train were slower by 6km/hr, it would have taken 6 hours more than the schedule time. Find the length of the journey. . (Ans)

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