# Solving Math Problems With Solutions

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Problem 7 The distance between two towns is 380 km.

At the same moment, a passenger car and a truck start moving towards each other from different towns. If the car drives 5 km/hr faster than the truck, what are their speeds?

They met at station C at 12 pm, and by that time the express train stopped at at intermediate station for 10 min and the freight train stopped for 5 min. Then the distance from station C to station A is $(148 - x)$ km.

By the time of the meeting at station C, the express train travelled for $\frac \frac$ hours and the freight train travelled for $\frac \frac$ hours.

Let's suppose that each of the four tractors ploughed $x$ hectares a day.

Therefore in 5 days they ploughed \cdot 4 \cdot x = 20 \cdot x$hectares, which equals the area of the whole field, 2880 hectares. Hence, each of the four tractors would plough 144 hectares a day.Then the second cow produced$(8100 - x)$litres of milk that year.The second year, each cow produced the same amount of milk as they did the first year plus the increase of \%$ or \%$.They decided to plant birches and roses at the school's backyard. If each girl planted 3 roses, there are$\frac$girls in the class. Therefore$\frac 3(24 - x) = 24x 9(24 - x) = 3\cdot 24x 216 - 9x = 72$6 - 72 = 8x$$\frac = x$$x = 18$ So, students planted 18 roses and 24 - x = 24 - 18 = 6 birches.While each girl planted 3 roses, every three boys planted 1 birch. Problem 14 A car left town A towards town B driving at a speed of V = 32 km/hr. Let us consider only the trip from C to B, and let $x$ be the number of hours the driver spent on this trip.b) By the time of the meeting at station C the freight train rode for $\frac \frac$ hours, i.e. Therefore it left station B at - (1 \frac) = 10 \frac$hours, i.e. So she increased her speed by 10 km/hr and she arrived at city B 36 minutes earlier than she planned. If she continued at the same speed she would be$ minutes late, i.e. So, she covered the distance between A and B in \frac$hr, and it was 36 min less than planned. When we equalize the expressions for the scheduled time, we get the equation:$\frac - \frac = 2 \frac \frac\frac = \frac\frac = \frac$x - 50 = 4x 200$ $x = 250$ So, the distance between cities A and B is 250 km.the planned time on the road is $\frac - \frac$ hr. Problem 12To deliver an order on time, a company has to make 25 parts a day.How many hectares a day would one tractor plough then?Solution: If each of $tractors ploughed 0$ hectares a day and they finished the work in $days, then the whole field is: 0\cdot 6 \cdot 4 = 720 \cdot 4 = 2880$ hectares.So 00 \frac\cdot x \frac \cdot (8100 - x) = 9100$Therefore 00 \fracx \frac(8100 - x) = 9100$$\fracx = 190$$x = 3800$Therefore, the cows produced 38 litres of milk the first year, and 70$and 30$ litres of milk the second year, respectively.Problem 10The distance between stations A and B is 148 km.

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