A bus takes 195 minutes to travel a distance of (2x + 30) km at an average speed of (x-20) km/h. Calculate the actual distance travelled. Give your answer in kilometers. (3 marks)

Muda uliotolewa ni 195 dakika. Ili kubadilisha kwenda masaa, tunagawanya kwa 60:

$$T = \frac{195}{60} \text{ masaa}$$ $$T = \frac{13}{4} \text{ masaa}$$

Fomula ni Umbali = Kasi $\times$ Muda ($D = S \times T$).
Tunapewa:
Umbali $D = (2x + 30)$ km
Kasi $S = (x - 20)$ km/h
Muda $T = \frac{13}{4}$ masaa

Weka thamani hizi kwenye fomula:

$$2x + 30 = (x - 20) \times \frac{13}{4}$$

Anza kwa kuzidisha pande zote mbili za mlinganyo kwa 4 ili kuondoa sehemu:

$$4(2x + 30) = 13(x - 20)$$ $$8x + 120 = 13x - 260$$

Kusanya $x$ upande mmoja na namba upande mwingine:

$$120 + 260 = 13x - 8x$$ $$380 = 5x$$

Gawanya kwa 5:

$$x = \frac{380}{5}$$ $$x = 76$$

Sasa tumia thamani ya $x = 76$ kwenye usemi wa umbali $D = (2x + 30)$ km:

$$D = 2(76) + 30$$ $$D = 152 + 30$$ $$D = 182 \text{ km}$$

Umbali halisi uliosafirishwa ni $\text{182 km}$.