₦airaland Forum

Solve and show workings

I will need part of the money to buy pen and exercise book to solve this down.

pimpchi:
Solve and show workings

(a) Given:
Speed for the journey = 380 km
Total time taken for the journey = 4hours

The journey was in two parts.
First part of the journey was on the motorway and the second part was on the country road

Let x and y represents the distance and time taken respectively for the journey in the first part (on the motorway);
Therefore, the speed on the motorway is calculated as x ÷ y = 110 km/h
x = 110y ...... Eqn 1

To get equation 2, let's find the expression for speed on the country road
Distance on the country road = 380km - x
Time spent on the country road = 4hrs - y
Therefore, the speed on the country road = (380 - x) / (4- y) = 70km/h,
380 - x = 70(4 -y),
380 - x = 280 - 70y,
380 - 280 = x - 70y,
x - 70y = 100 ....Eqn 2

Therefore, these are the simultaneous equations
x = 110y ...Eqn 1
x - 70y = 100 ...Eqn 2


(b) Solving the equations;
Sub for x in eqn 2 using eqn 1,
x - 70y = 100,
110y - 70y = 100
40y = 100
y = 100/40 = 2.5 hours

sub for y in eqn 1,
x = 110y,
x = 110 (2.5),
x = 275km
Therefore the distance covered on the motorway is 275km

@pimpchi
Feel free to ask questions.

I couldn't even get past speed 110km/h

dejt4u:
(a) Given:
Speed for the journey = 380 km
Total time taken for the journey = 4hours

The journey was in two parts.
First part of the journey was on the motorway and the second part was on the country road

Let x and y represents the distance and time taken respectively for the journey in the first part (on the motorway);
Therefore, the speed on the motorway is calculated as x ÷ y = 110 km/h
x = 110y ...... Eqn 1

To get equation 2, let's find the expression for speed on the country road
Distance on the country road = 380km - x
Time spent on the country road = 4hrs - y
Therefore, the speed on the country road = (380 - x) / (4- y) = 70km/h,
380 - x = 70(4 -y),
380 - x = 280 - 70y,
380 - 280 = x - 70y,
x - 70y = 100 ....Eqn 2

Therefore, these are the simultaneous equations
x = 110y ...Eqn 1
x - 70y = 100 ...Eqn 2


(b) Solving the equations;
Sub for x in eqn 2 using eqn 1,
x - 70y = 100,
110y - 70y = 100
40y = 100
y = 100/40 = 2.5 hours

sub for y in eqn 1,
x = 110y,
x = 110 (2.5),
x = 275km
Therefore the distance covered on the motorway is 275km

@pimpchi
Feel free to ask questions.

Wrong

pimpchi:
Wrong

He's right. To simplify the solution, if you work out 380= 110y + 70(4-y); where y = amount of time spent on the motorway, you get 275km (2.5hours × 110km/h) on the motorway and 105km (1.5hours × 70km/h on the country road); which is what he gave. His derivation of the two equations is also correct.

pimpchi:
Wrong

lol. the solution is what I have provided for you