Question

1. A man travels 70km at a certain average speed on a dual carriage way. He then reduces his speed by 30km\h to cover a distance of 50km on a bad road. If the time taken is the same for both parts of the journey, calculate
a. His average speed for each part of the journey
b. The average speed for the whole journey


2. A girl went to shop to buy pineapple and apple .a pineapple costs #2 more than an apple.the girl bought as many pineapples for #60 as she bought pineapples for #54.how much does a pineapple and an apple cost together

3. The sum of the ages of Mr Daniel and his daughter is 60 years.5 years ago the ratio of their ages was 1:4
a. how old are the now
b. find the difference between their ages

Answer 1

Answer on Question #84604 – Math – Algebra

Question

1. A man travels $70\,\text{km}$ at a certain average speed on a dual carriage way. He then reduces his speed by $30\,\text{km}\backslash h$ to cover a distance of $50\,\text{km}$ on a bad road. If the time taken is the same for both parts of the journey, calculate

a. His average speed for each part of the journey

Solution

Let $t$ is time of each part of journey, $v$ is average speed on the first part of journey; then:

$$t = \frac{70}{v} = \frac{50}{v - 30}$$ $$70 \cdot (v - 30) = 50\,v$$ $$20\,v = 2100$$ $$v = 105\,\text{km/h}$$

The average speed on the second part of journey:

$$v_1 = 105 - 30 = 75\,\text{km/h}$$

Question

b. The average speed for the whole journey

Solution

$$t = \frac{70}{105} = \frac{2}{3}\,h$$ $$v_0 = \frac{70 + 50}{2 \cdot 2/3} = \frac{3 \cdot 120}{4} = 90\,\text{km/h}$$

Question

2. A girl went to shop to buy pineapple and apple. A pineapple costs #2 more than an apple. The girl bought as many pineapples for #60 as she bought pineapples for #54. How much does a pineapple and an apple cost together?

Solution

Let $n$ is the number of pineapples or apples, $x$ is price of apple; then:

$$(x + 2)n = 60$$ $$xn = 54$$ $$\frac{x + 2}{x} = \frac{60}{54} = \frac{10}{9}$$ $$9 \cdot (x + 2) = 10x$$ $$x = 18\#$$ $$C = x + (x + 2) = 18 + 20 = 38\#$$

3. The sum of the ages of Mr Daniel and his daughter is 60 years. 5 years ago the ratio of their ages was 4: 1

Question

a. how old are the now

Solution

Let $x$ be the age of Mr Daniel, $y$ be the age of his daughter; then:

$$x + y = 60$$ $$\frac{x - 5}{y - 5} = 4$$ $$x = 60 - y$$ $$\frac{60 - y - 5}{y - 5} = 4$$ $$60 - y - 5 = 4y - 20$$ $$5y = 75$$ $$y = 15$$ $$x = 60 - 15 = 45$$

Question

b. find the difference between their ages

Solution

$$x - y = 45 - 15 = 30$$

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