David is planning to travel alone by motorcycle from Singapore to China. The total distance to be travelled is 4900 km. In the first week, he can travel 1000 km.
a) How many weeks does it take for David to reach his destination, if he reduces the distance travelled by 100 km every week due to fatigue?
b) What is the distance he travels on the last leg of his journey?
1000 + 900 + 800 + 700 + 600 + 500 + 400 = 4900
To answer the first question, we need to calculate the number of weeks it takes for David to reach his destination by considering the distance he can travel each week and the reduction in distance due to fatigue.
To calculate the number of weeks, we can set up an equation:
Distance traveled each week = 1000 km - 100 km * Number of weeks traveled
Let's solve this equation:
1000 - 100w = 4900
where w represents the number of weeks traveled.
Rearranging the equation:
100w = 1000 - 4900
100w = -3900
w = -3900 / 100
w = -39
Since the number of weeks cannot be negative, we can conclude that it is not possible for David to reach his destination following this scenario.
Therefore, the answer is that it is not possible for David to reach his destination by reducing the distance traveled by 100 km every week due to fatigue.
For the second question, we need to determine the distance David travels on the last leg of his journey. Since we established that he cannot reach his destination by reducing the distance traveled by 100 km every week due to fatigue, we cannot determine the distance traveled on the last leg.